Martianus Capella
The Marriage of Philology and Mercury

/215/

Book VI
Geometry

→ lat [575] “I am grateful to you, O Goddess, and shall ever be obliged to render thanksgiving to you for deigning to nod your eminent⁹ head in approval of our desires. I acknowledge and respect what I have witnessed. Even now a select coterie of ladies are appearing, ready to offer service to the discipline. They are bearing a beautiful little board colored with a sprinkling of greenish powder; and they take their place, with obvious self-assurance, in the midst of the celestial senate. But who those ladies are, and what they are bearing, I do not perceive, unacquainted as I am with what is going to transpire.”

→ lat [576] At this point Satire, in her usual charming manner, an attentive listener to my entire story from the very beginning, playfully remarked: ‘Unless I am mistaken, my Felix, you have needlessly used up more than enough oil to anoint whole palaestras,¹⁰ or at least the school of the groom himself; and Mulcifer [Vulcan] has burned up your allotment of wick – to no avail, since you do not recognize Philosophy, mother of so many scholars and men so illustrious.¹¹ /217/ When, not long ago, Jupiter called upon her to promulgate a decree of the celestial senate and, in seeking a marriage partner for Philology, dispatched her to address the suitor [Mercury] on the subject of matrimony, even then were you unable to recognize her?

→ lat [577] “But because now you are wise as an Arcadian or a Midas,¹² particularly since the time when your feverish exertions and devotions to the wrangling and pettifoggery of the courts¹³ tied you down and blunted your edge for better occupations, you seem to have forgotten all about this lady, and wish to take no notice of her sister. → lat [578] Now the lady over there, prepared to perform equally important functions, as you observe, is called Paedia [Learning],¹⁴ a very well-to-do woman, who regards the wealth and treasures of a Croesus or a Darius as contemptible alongside her own. Philosophy, as one fully aware of her own endowments and rarely in attendance at plenary gatherings, proudly refusing to present glimpses of herself to anyone – at least amongst the leaders – nevertheless has frequently tarried behind, and smiled at the starveling philosophers, particularly the ones she sees barefoot, or those shaggy with uncut hair, or [those with] bodies half covered with filthy mantles.¹⁵ In fact, if you except Marcus Terentius [Varro] and a few other Romans of consular rank, there is no one else whose threshold she has crossed. → lat [579] You notice the haughty and austere look on the faces of both ladies; even so, both of them, attendants of Mercury’s bride, shortly to arrive, are being readied for their duties.

“That object which the women brought in is called an abacus board,¹⁶ a device designed for delineating figures; upon it the straightness of lines, the curves of circles, and the angles of triangles /218/ are drawn. This board can represent the entire circumference and the circles of the universe, the shapes of the elements, and the very depths of the earth; you will see there represented anything you could not explain in words.”

I replied: “The woman soon to appear doubtless surpasses Apelles and Polyclitus;¹⁷ indeed, she is so highly reputed to be able to represent any object that we must conclude that she is the offspring of Daedalus, of Labyrinth fame.”

→ lat [580] Immediately there came into view a distinguished-looking lady,¹⁸ holding a geometer's rod in her right hand and a solid globe in her left. From her left shoulder a peplos was draped, on which were visible the magnitudes and orbits of the heavenly bodies, the dimensions, intersections, and outlines of the celestial circles, and even the shadow of the earth, reaching into the sky and giving a dark purplish hue to the golden orbs of the sun and the moon amidst the stars. → lat [581] The peplos itself glistened with the sheen of the vernal sky;¹⁹ it was marked with many figures – to serve the purposes of her sister Astronomy as well – numbers of various kinds, gnomons of sundials, figures and designs showing intervals, weights, and measures, depicted in many colors.²⁰ This tireless traveler was wearing walking shoes, to journey through the world, and she had worn the same shoes to shreds in traversing the entire globe. → lat [582] She entered the senate of the gods. Though she could have told at once how many stadia and fathoms, down to the inch, she had measured in the distance between the earth and the celestial sphere,²¹ instead, moved by the majestic appearance of Jove and the heavenly company, she hastily made her way to the uncovered abacus board, glancing about at the adornment of the outer canopy and the palace studded with constellations.

→ lat [586] Geometry finally broke the spell of her rapt admiration of the glittering heavens and turned her eyes to regarding the gods about her, with a reserve becoming a dignified lady who enjoyed the respect of all and was considered mistress of the other arts which /220/ are known to the gods. A request was made that she begin disclosing the secrets of her knowledge, from the very beginning. As she brushed aside a lock of hair, her face shone with distinction and majesty. → lat [587] She began drawing diagrams on the powdery surface of her abacus and spoke thus: “I see my Archimedes and the most learned Euclid among the philosophers present. I could call upon them to expound my doctrines to you at length, to ensure that every matter is expertly explained and no veil of obscurity is interposed. However, I deem it more appropriate, on this occasion which calls for²⁶ rhetorical skill, to disclose these matters to you myself, as best I can, in the Latin tongue, something that rarely happens in this field. Those men, in fact, speak no Latin, and expound what I have taught them only in Greek.

→ lat [588] “First, I must explain my name, to counteract any impression of a grimy itinerant coming into this gilded senate chamber of the gods and soiling this gem-bedecked floor with dirt collected on earth. I am called Geometry because I have often traversed and measured out the earth, and I could offer calculations and proofs for its shape, size, position, regions, and dimensions. There is no portion of the earth’s surface that I could not describe from membry.”

→ lat [589] Now inasmuch as many present in the celestial senate had not been born on earth and said that they had never trodden upon the earth, and since Jupiter as well was eager to investigate all the hiding places on earth – for the reason, I suppose, that no beautiful girl of that epoch, either, might escape that lecher of many transformations – Geometry therefore was bidden to expound this first, and then to reveal the other precepts of her discipline. She began her discourse as follows:

→ lat [590] “The shape of the earth is not flat, as some suppose who imagine it to be like an expanded disc; nor is it concave, as others suppose who have spoken of the rains ‘descending into the lap of Mother Earth.’²⁷ Rather it is rounded – even spherical – as /221/ Dicaearchus²⁸ maintained. → lat [591] For the rising and setting times of the stars would not vary according to the elevation or sloping of the earth if the operations of the heavenly firmament were spread out above a flat surface and the stars shone forth over earth and seas at one and the same time; or, again, if the rising of the sun were concealed from the hollowed cavities of the more depressed parts of the earth.

→ lat [592] Since the latter supposition may be disregarded as a worthless opinion, it behooves us to examine the former opinion, to which even the natural philosopher Anaxagoras gave his approval,²⁹ even though he is believed to have supported it with some arguments. Indeed, he says that the flatness of the earth is clearly proved by the risings and settings of the sun and the moon: as soon as the first flash of radiance has appeared above the horizon, the beams are immediately directed to our eyes in straight lines; the proof of this phenomenon becomes more evident when we get clear of the obstacles of mountains and take a position on a seashore beach. Now if Anaxagoras’ opinion were true, celestial bodies, on rising above the horizon, would become visible to inhabitants of all lands at the same time and, on being hidden beneath the horizon, would be able to cover all lands with darkness in one setting. In that case the observation of the Roman bard would be controverted when he says: ‘While rising Sun first breathes on us with panting steeds, / Down there the evening Sun is red with waning light.’³⁰ → lat [593] Besides, all nights and days would correspond, their intervals and hours always being equal, and in no portion of the earth would some stars be visible and others be obscured.

But when the constellation of the Great Bear wheels overhead in Italy it is completely buried from view and unknown to the Troglodytes and to adjacent inhabitants in Egypt. The brilliant stars Canopus and Crinis Berenices [Berenice’s Hair] are not seen in Scythia, Gaul, and, in fact, in Italy; yet in antarctic regions they /222/ are conspicuous stars and are seen almost directly overhead.... Alexandria, Canopus is elevated above the horizon by a quarter of one interval,³¹ but the Triones [Ursa Major and Ursa Minor] are not visible because of the slope. In Arabia, in the month of November, Helix [Ursa Major] is not visible at nightfall, but becomes visible during the second watch;³² in Meroe, at the summer solstice, it is barely visible for a brief space of time, when it rises at dawn about the time of the rising of Arcturus.³³ Likewise, in India, it is seen in the port of Patavitano³⁴ only in the early evening, and on Mount Maleus it is visible for only fifteen days each year. Who, then, would doubt that the obstruction of the curving slopes of the spherical earth causes some constellations to be hidden from view while others emerge clearly above the slopes?

→ lat [594] For those who doubt the sphericity of the earth, additional evidence is found in the fact that eclipses of the sun and the moon occurring in the west are not seen by inhabitants of the east, and, similarly, inhabitants of Britain and of western lands are not aware of eclipses that occur in the east. In regions in between, the times of eclipses vary by hours. Servius Nobilis³⁵ reported that, at the victory of Alexander the Great in Arabia, the moon was eclipsed at the second hour of the night, whereas in Sicily this eclipse was observed as the moon was first rising. An eclipse of the sun that took place during the consulship of Vipstanus and Fonteius, on April 21,³⁶ /223/ was seen in Campania in the seventh hour and was verified as occurring in Armenia during the eleventh hour of the same day. These discrepancies are the result of the sloping surface of the spherical earth.³⁷ → lat [595] Finally, hemispherical bowls which are called horologia, or sundials, are adjusted according to variations in latitude. Gnomons are replaced at distances beyond five hundred stadia,³⁸ as the shadows are depressed or elevated according to the location of the dials. Consequently, the longest day of the year at Meroe lasts twelve and two thirds hours, at Alexandria fourteen, in Italy fifteen, and in Britain seventeen. At the summer solstice, when the sun is borne toward the celestial pole, it bathes the regions that lie beneath in continuous daylight; but when it makes its wintry descent, it causes northern regions to shiver in darkness that lasts six months. Pytheas of Massilia reported that he found such a condition on the isle of Thule. Those discrepancies of the seasons, unless I am mistaken, compel us to admit that the earth is round.

→ lat [596] We must now reveal the size of the earth and what position it holds in the universe. Eratosthenes, a most learned man, used a gnomon in calculating the earth’s circumference as 252,000 stadia.

→ lat [597] There are bronze hemispherical bowls called scaphia, which mark the passage of the hours by means of a tall, upright stylus, located at the center of the bottom of the bowl. This stylus is called a gnomon. The length of its shadow, measured at the equinox by a determination of its distance from the center, when multiplied twenty-four times, gives the measure of a double circle.³⁹ → lat [598] /224/ Eratosthenes, upon being informed by official surveyors in the employ of King Ptolemy as to the number of stadia between Syene and Meroë,⁴⁰ noted what portion of the earth’s surface that distance represented; and multiplying according to the proportionate amount, he straightway determined how many thousands of stadia there were in the earth’s circumference.

→ lat [599] So much for a brief account of the determination of the earth’s dimensions. Now let us reveal its position. That the earth stands stationary at the middle and bottom of the universe is demonstrated by several arguments. First, it was in the very same position, from which it could not be moved, before the universe was founded. Hence, when the elements of the primal mixture were separated from each other, the vast and voluble expanse of waters and the diffusion of the atmosphere spread all about the stationary earth and hemmed it in, making that which was enclosed within the rounded and voluble substance the middle portion. Or again, everything that is the middle in a sphere becomes the bottom, since whatever supports lines that are equidistant from the surface of a sphere is compressed by them.⁴¹ → lat [600] That which is lowest must come to a halt by the very extremity of its position, for there is no place below where it can fall. All weights fall downward upon the earth – rain, hail, snow, lightning – the ocean, too, which sinks into the nethermost parts of the earth, and the darkling streams that ‘welter in the bottommost abyss.’⁴² The earth, which supports the floods and all /225/ other weights, you see, is compressed on all sides and has nothing beneath it, to which it may retire. It must be assumed to be at the middle, since it holds the last position.

The intervals of time at the equinox are a clear proof of this truth: water clocks show that the hours of the forenoon and the afternoon and of the day and the night are of equal duration.⁴³ → lat [601] Another proof that the heavens are equidistant on all sides from the earth is found in the two solstitial circles: the length of the day, when the sun reaches its highest point in the heavens, is equal to the length of the night, when the sun descends to the winter solstice. Similarly, the length of daylight allotted under each of the signs of the zodiac corresponds to the length of darkness occurring when the sun is in the opposite quarter. This goes to prove that the celestial circles and the constellations are equidistant from us in all directions, and that the earth is at the middle. If this topic seems to have been adequately discussed, I shall now proceed to name the zones of the earth, all of which I myself have traversed.

→ lat [602] The earth’s surface is divided into five zones, or belts, marked by differences in their conditions. Intemperate conditions of excessive heat or cold render three of the belts uninhabitable.⁴⁴ The two zones that border upon the north and south poles have reason to be deserted, with their enormous chill and cold, and severe snowfalls; the belt in the middle is scorched by fires and stifling heat, and burns all living things that draw near. The two belts between, tempered by the exhalations of life-giving breezes, are conducive to human and animal habitation. These belts, of course, curve entirely about the spherical earth and gird the lower as well as the upper hemisphere.

→ lat [603] You must know that the earth is divided into two distinct parts, or hemispheres: there is an upper hemisphere, which we inhabit and which Oceanus encircles; and there is a lower hemisphere. The upper one begins at the place of the sun’s rising, the lower one at the place of its setting. The Greeks have given the name horizon /226/ to the circle of demarcation. → lat [604] Now, inasmuch as the five zones encompass both parts, upper and lower, they actually form ten regions. The one inhabited by us extends northward. Another, tending southward, is believed to be inhabited by men called antecians (antoikoi). → lat [605] Correspondingly, there are two habitable regions in the lower hemisphere. Those diametrically opposite us are called antipodes and those who are diametrically opposite our antecians are called antichthones.

Our condition is distinct from theirs in the oppositeness of our seasons. When we are scorched with summer’s heat, they are numbed with cold; when spring here bedecks the meadows with flowers, the heat of summer there is yielding to the gentle warmth of autumn; when we have our shortest day, they have their longest; we get a clear view of Arctos [the Bear], which is wholly invisible to them.⁴⁵ → lat [606] Our antipodes experience with us a common period of winter and the heat of summer, but we have our days and nights at opposite times from them: that is, long days in summer and long nights in winter for us, and long nights in summer and long days in winter for them. Septentrio [the Great Bear] is visible to us, but always lies hidden from them. The same is true of tfre earth’s inhabitants who are called antecians: they and their antipodes experience the four seasons of the year in common, and they alone have a view of the south pole, which is ever invisible to their antipodes and to us.⁴⁶ → lat [607] Those who inhabit the middle belt observe daily variations in risings and settings. For those who have the sun overhead, its rising is swifter and its setting slower. At the time of the equinox, risings and settings are alike, and there are no stars that are not visible to them; stars that rise at the same time also set together. Inhabitants here have their days equal to their nights, and objects cast no shadows at noon. Their antipodes also have days and nights of equal length. Since the sun, in its haste to reach its northern solstice, draws its path across these inhabitants, and again passes them by as it moves to its winter solstice, receding far from them on either side, it is /227/ undoubtedly true that they experience two summers⁴⁷ and two winters each year. When the sun is rising for them, it is setting for their antipodes.

→ lat [608] But the two regions, or belts, referred to above – one of which is covered with ice because of its proximity to the chill of Plaustrum [the Wain], the other deserted because of antarctic winds – do not have antipodes of their own.⁴⁸ However, because of their diametrically opposite locations, they become antipodal to each other. Inhabitants here observe no risings of the celestial bodies, except the planets, which do not course over their heads but have risings near the middle of one side.⁴⁹ Fixed stars are visible for six months, and for six months they are out of sight. The equator is the circle that marks risings for them, and only six signs of the zodiac are visible. Days and nights are of six months’ duration, and the poles are visible directly overhead.⁵⁰ But the one region, adorned with the luster of Septentrio, and the other, with the star Canopus, have no acquaintance with the remaining portions of the sky. → lat [609] That most learned man Pytheas has disclosed what conditions are like in those regions; but I myself have traversed them: there is no portion of the earth’s surface that is not known to me.⁵¹ The full measurement of the earth’s circumference – to convert into Roman miles the figure in stadia which I recorded in the calculation above – is thirty-one thousand five hundred miles.⁵² At this point it would be well to include the opinion which Ptolemy records in his Geography.⁵³ → lat [610] He cuts the circumference of the zodiac /228/ into three hundred and sixty segments of the sky. Each segment, when brought down toward the earth’s center, according to him, stretches across the earth’s surface a distance of five hundred stadia. Each stadium is equal to one hundred and twenty-five paces. Multiplying by the five hundred stadia that are measured in each segment, we obtain a figure of sixty-two thousand five hundred paces. The same five hundred stadia, multiplied by three hundred and sixty, give a figure of one hundred and eighty thousand stadia for the entire circumference. Next, multiplying by the number of paces in one stadium, as recorded above, we get a figure of twenty-two thousand five hundred miles for the earth’s circumference.⁵⁴ So much for our disclosures about the globe of the entire earth.

→ lat [611] Now the length of the earth from east to west – that is, from the farthest part of India itself to the pillars consecrated to Hercules at Cadiz – is eight thousand five hundred and seventy-seven miles, according to one authority, Artemidorus.⁵⁵ Isidore,⁵⁶ in fact, says that the distance is nine thousand eight hundred and eighteen miles. But then again Artemidorus adds to his aforementioned figure the territory beyond Cadiz. He notes that that land extends along the perimeter of Spain, around the ‘sacred promontory,’⁵⁷ as far as the last of the capes, called the Artabrian promontory,⁵⁸ a distance of nine hundred and ninety-one miles.

→ lat [612] The total dimensions can be shortened by traveling over the seas. From the Ganges River and its mouth, where it flows into the eastern Ocean, across India and Parthia to the Syrian city of Myriandrus, on the Gulf of Issus [Iskenderun Korfezi], the distance is five thousand two hundred and fifteen miles. From there, by the shortest sea route, to Cyprus, then to Patara in Lycia, Rhodes, the island of Astypalaea in the Carpathian [Aegean] Sea, then to Taenarum in Laconia, and on to Lilybaeum in Sicily and Caralis /229/ [Cagliari] in Sardinia is three thousand four hundred and fifty miles; from there to Cadiz is four thousand two hundred and fifty miles. The total distance from the eastern Ocean is eight thousand five hundred and seventy-eight miles.⁵⁹ → lat [613] Another route can be taken over land and sea: along the Ganges and Euphrates rivers, across Cappadocia and Phrygia, over the Aegean and Laconian seas and the other gulfs to the Peloponnesus, on to Leucas, Corcyra, Acroceraunia, Brundisium, and Rome, across the Alps and Gaul, over the Pyrenees to the western Ocean, down the coast of Spain to Cadiz – a total distance of eight thousand six hundred and eighty-five miles. My estimate is corroborated by Artemidorus. Thus you have the length of the earth calculated by various methods.⁶⁰ → lat [614] The breadth of the lands from the southernmost region to the northern limits is very much smaller, inasmuch as it is contracted on either side by the excessiveness of the intemperate climates. What is more, on the northern side the rude and uncivilized nation of the Sarmatae prevents explorers from determining dimensions there. Nevertheless, all the regions that intrepid explorers have been able to penetrate have been adequately measured, and the breadth of the inhabited earth has been found to be almost one half smaller than the reckoning of its length. → lat [615] It has been determined that the breadth is five thousand four hundred and sixty-two miles. This measurement is taken from the shores of the Ethiopian Ocean, which is the farthest limit of habitation, to Meroe, thence to Alexandria, Rhodes, Cnidus, Cos, Samos, Chios, Mytilene, Tenedos, the cape of Sigeum [Kumkale], the entrance to the Pontus [Black Sea], the cape of Carambis [Kerempe], the entrance to the Maeotis [Sea of Azov], and the mouth of the Tanais [Don River]. This measurement, if it is taken across the open seas, is reduced by six hundred and seventy-eight miles. → lat [616] Artemidorus maintained that this was the farthest extent of geographical knowledge; but Isidore added one /230/ thousand two hundred and fifty miles, as the distance to Ultima Thule, which seems to me to be an unreliable opinion. For I assert that the earth has as much breadth as it has length. We offered above a demonstration and proof that the orb of the earth is round, and it is impossible for a globe to have unequal sides. The authorities mentioned above have declared the earth’s surface to be habitable.⁶¹ → lat [617] Voyages in all directions prove that a circumambient ocean girds the shores of the globe.⁶² The entire western coast, winding around Spain and Gaul from Cadiz, is navigated these days. → lat [618] During the time that the late emperor Augustus was sailing around Germany with his fleet, he traversed the entire northern Ocean. First he reached the Cimbrian promontory [Denmark], and from there he crossed a great sea and got as far as Scythia and its frozen waters. → lat [619] Similarly, with regard to the distant eastern borders and the Indian Ocean, Macedonian fleets, during the reigns of Seleucus and Antiochus, cruised along the shores that verge into the Caspian Sea. Lake Maeotis is considered a bay of the same ocean. Of a like kind are the reports of the seas flowing around the left-hand side⁶³ of the earth’s habitations. → lat [620] From the pillars consecrated to Hercules at Cadiz all the way around to the Arabian Gulf, the southern Ocean is navigable, as has been attested in many instances. → lat [621] The victories of Alexander carried his fleet over the greater part of this sea. When Gaius Caesar, the son of Augustus,⁶⁴ was /231/ stationed in this same Arabian Gulf, the shipwrecked hulls of Spanish ships were discovered here, together with other fragments that had been cast ashore. Hanno, at a time when the Carthaginian Empire was at its height, sailed around Mauretania [Morocco] and from there turning south, in a very long voyage, reached the borders of Arabia.⁶⁵ Cornelius [Nepos] is our authority for the report that a certain Eudoxus, escaping from the evil designs of his king, fled from Arabia to gain asylum at Cadiz. Caelius Antipater reports that he saw a man who, in his eagerness for trade, had sailed from Spain to Ethiopia. The same Cornelius, after taking some Indians captive, sailed past Germany.⁶⁶ → lat [622] I consider the fact that the seas have been navigated on all sides to be proof that the lands of the upper hemisphere are girded by a sea that stretches over a circular course.

I shall now discuss the divisions of the earth, insofar as this brief account allows. The entire expanse of habitable land in the upper hemisphere is divided, according to most authorities, into three continents: Europe, Asia, and Africa. The first and last of these continents are separated by an irruption of the Ocean; → lat [623] for the mighty flood of the Atlantic, cutting through the depths of land from the Strait of Cadiz [Gibraltar], cleaves the African from the Iberian shore and pours itself rapidly into the waters of the adjacent sea. Lengthwise the strait extends scarcely fifteen miles, from the opening toward Cadiz to the entrance of the inner sea. The breadth at the narrows is five miles, at a wider point seven miles, and at the widest point ten miles. Through the strait poured a deluge of crashing waters swollen by different seas, engulfing the various bays and subsiding plains.

→ lat [624] This onrush of the invading Ocean created the European continent on the left hand and the African continent on the right, and terminated them with mountains on either side. For the sea is kept from Europe by Mount Calpe [Gibraltar] and from Africa by /232/ Mount Abinna [Ceuta]⁶⁷ which, looming on either side, deserve to be called the pillars of Hercules because in the testimony of antiquity the bounds of his labors were immortalized by them, since the impassable limits of the world prevented him from advancing further. → lat [625] Here, too, is evidence of the power of his divine strength: whereas, heretofore, nature used to keep the seas and the lands apart and to confirm that fact by the great encircling belt of Ocean, Hercules, sundering the above-named mountains by their roots and breaching the barrier, admitted the sudden flood to the low-lying fields and the hollows of the earth’s surface, providing a challenge to the energies of mankind, changing the earth’s features and the decrees of nature.

→ lat [626] To the left of this strait, Europe stretches, as far as the waters of the river Tanais. Here Asia begins, and in turn is bounded by the Nile River. This Nile severs Asia and Africa and divides the land around itself with numerous tributaries. However, very many authorities have said that the European continent terminates at the entrance to the Propontis, and that the Propontis, flowing down through narrows, extends to Lake Maeotis.⁶⁸ → lat [627] The starting point and commencement of Europe is assigned to Spain, a fruitful and rich province, famous for its production of metals and gold, red lead, marble, and gems. Because the river Hiberus [Ebro] flows through it, this land has acquired the name of its river [Iberia]. The part of Spain that borders on the Atlantic and extends along the shores of the Strait of Cadiz [Strait of Gibraltar] is called Baetica, also taking its name from that of a river; the region extending closer [to Italy], from the territory of the Oretani,⁶⁹ is called Tarraconensis from the city of Tarraco, /233/ which the Scipios founded. The Carthaginians established Cartagena, calling towns, wherever they founded them, by names familiar to them. → lat [628] But the area alongside that aforementioned is constituted as another province from the Pyrenees Mountains, in that Lusitania adjoins Baetica along its northern border. Legend has it that Lusitania got its name from the sport (lusus) of Liber [Bacchus] or of those who reveled with him.⁷⁰ This province is also penetrated by a river which has its own name, although the Tagus also brings fame to the province because of its auriferous sands. → lat [629] They say that Ulysses founded the town of Olisipo [Lisbon]⁷¹ there, which gave its name to the promontory that separates the seas from the land. The Gallic sea and the northern ocean have their beginning as they bend around this projection, and the Atlantic and western oceans come to an end here, delimited by the extrusion of Spain. In that territory, mares are impregnated by the winds, Favonius himself endowing their offspring with swift flight.⁷² → lat [630] Baetica surpasses the other provinces in fertility. It has two jurisdictions, that of Cadiz and that of Cordoba, and has one hundred and seventy-five well-inhabited towns.⁷³ → lat [631] In length it stretches from the confines of the town of Castulo to the town of Cadiz, a distance estimated at more than two hundred and fifty miles; its breadth is two hundred and twenty-four miles.⁷⁴ → lat [632] The entire province has seven jurisdictions: those of Cartagena, Tarragona, Caesaraugusta [Saragossa], Clunia, Asturia [Astorga,] Lucus Augusti [Lugo,] and Bracara Augusta [Braga]. In addition to islands and communities dependent on others, numbering two-hundred and ninety-four, it contains one hundred and /234/ seventy-nine towns.⁷⁵ It extends, according to Marcus Agrippa’s calculations, four hundred and seventy-five miles in length and two hundred and twenty-four miles in breadth, when the boundary is carried as far as Cartagena.⁷⁶ This figure of Agrippa constitutes no small error, → lat [633] for all of Hispania Citerior (Hither Spain] from the Pyrenees to the confines of Castulo stretches six hundred and seven miles in length; and the figure is a little more along the coast. The breadth is estimated to be three hundred and seven miles from Tarraco to the shore at Oasso [San Sebastian], at the foot of the Pyrenees, where the land is hemmed in by the sea on either side. As the land gradually extends outward, it adds appreciably to the breadth.⁷⁷ → lat [634] This same Pyrenees range on the other side forms a boundary of the territories of the Gauls. The land extending from the foothills of the Pyrenees to the Rhine River and from the Ocean to the Cevcnnes and the Jura has been allotted to the Gauls. Besides, there is a province called Narbonensis, formerly called Bracata, which is washed by the Mediterranean. It is separated from Italy by the ranges of the Alps⁷⁸ and by the Var River. The length of this province, according to Agrippa’s measurements, is three hundred and seventy miles and its breadth two hundred and forty-eight miles. → lat [635] The Rhone River flows in this province, rising in the Alps and passing through Lake Leman [Lake Geneva]. It bring fertility in crops and livestock to the lands. Its mouths have different names: one is called the Spanish, another the Metapinic; and the third, which has a fuller flow, is called the Massiliotic. The province is famed⁷⁹ /235/ for its manhood, towns, and produce, and it has only one shame to be mentioned, the fact that formerly it was considered right to perform human sacrifice there.⁸⁰ → lat [636] On the other side of the Alps, where the slope stretches out and is bathed in the rays of the rising sun, Italy begins its descent – a country extolled by the ancients far more than all others for the beauty of its city of Rome. → lat [637] The Ligurians are the first nation across the border; next the sacred region of Etruria occupies a fertile soil, a land famed for its compact with the hero Aeneas,⁸¹ as well as for its discovery of remedies and for the unearthing of Tages.⁸² Next come the Umbrians and Latium and the mouth of the Tiber, and then the capital of the nations, Rome herself, as long as she was in her prime,⁸³ a city to be extolled to the skies for her military prowess, men, and religious worship. Rome is situated sixteen miles from the coast. → lat [638] The next stretch of coast is held by the Volscians and named after them; then, in succession, Campania, the Picentes, the coast of Lucania, and Bruttium. The peninsula of Bruttium faces the sun and wind of the south and juts out into the sea, and with an arm going out to the left [Calabria] it embraces the waters of an enclosed bay [the Gulf of Taranto]. So, if from the edge of the Alps you look down to the right and the arm of long mountain [the Apennine range], putting out spurs on either side, you seem to see a kind of theater of water [the Tyrrhenian Sea].⁸⁴ Italy, indeed, is crescent-shaped,⁸⁵ and extends in a half-circle down /236/ to the aforementioned promontory. To sum up, starting at Cadiz, where the jaws of the strait open, to the Bruttian gulf, the first in Europe, the inflowing seas are quiet.

→ lat [639] On the interior side the land extends northward, into the Upper [Adriatic] sea, along the coast of [Magna] Graecia, and is inhabited by the Sallentini, Pediculi, Apuli, Peligni, Istri, Liburni, and other less well-known peoples.⁸⁶ The land bends to the left and, with two promontories, assumes the shape of an Amazon's shield,⁸⁷ having Leucopetra on the right projection and Lacinium on the left. Although its lengthwise measurement, from the Alps at Augusta Praetoria⁸⁸ through Rome and Capua, down to the town of Rhegium, and not including the curvature backward, is one thousand and twenty miles; nowhere does its breadth exceed three hundred miles.⁸⁹ The distance from Italian soil to Istria and Liburnia is one hundred miles; from Epirus and Illyricum fifty miles; from Africa, according to Varro,⁹⁰ less than two hundred miles; from Sardinia one hundred and twenty; from Sicily one and a half miles; from Corcyra less than eighty miles; and from Issa fifty. → lat [640] The entire circuit of Italy is two thousand and forty-nine miles.⁹¹ Its central point is said to be in the district of Reate.⁹² Its narrowest point is at the port that is called Castra Hannibalis [Hannibal’s Camp]; here it is scarcely 40 miles wide.⁹³ Italy is also famous for the Padus [Po] River, known to the Greeks as the Eridanus. This stream originates in a remarkable spring on Mount Vesulus [Viso], one of the loftier peaks of the Alps; it becomes a river in the territory of the Ligurians; then /237/ the river submerges deep under the ground and emerges again in the vicinity of Forum Vibi. Its volume increases at the rising of the Dog Star; for when the snows on the Alps have melted in the heat of the summer sun, the river overflows its banks and, surpassed by none of the famous streams, it picks up thirty streams in its course and, swelling to an immense size, pours into the Adriatic Sea.⁹⁴ → lat [641] There are other memorable features of Italy, lauded by the poets: the town of Scyllaeum⁹⁵ and the Crateis River,⁹⁶ which was the mother of Scylla; the writhing whirlpool of Charybdis; the rose gardens of Paestum;⁹⁷ the cliffs of the Sirens; and the lovely glades of Campania, long famous; then the Phlegraean Fields and Tarracina, the dwelling place of Circe, formerly an island, now joined to the mainland. Rhegium is separated from Sicily, which has been detached into an island to compensate for the annexation of the island at Tarracina; then there is also Formiae, famed as the abode of the Laestrygonians.⁹⁸ → lat [642] At this point I could run through the names of the founders of cities: for example, Janiculum, named from Janus; Latium from Saturn,⁹⁹ Ardea from Danae,¹⁰⁰ Pompeii from Hercules, when he was leading a procession of Spanish oxen.¹⁰¹ Also connected with Hercules’ labors are the fields in Liguria known as the Campi Lapidarii [Lapidei; ‘Stony plain’] because, according to legend, the sky rained rocks when Hercules was fighting there.¹⁰² He also gave /238/ the Ionian Sea its name, because he slew Io, the daughter of Auto-clus, while she was engaging in highway brigandage. Iapyx, the son of Daedalus, founded Iapygia; Dardanus founded Cora; the Pelasgians, Agyllina;¹⁰³ and Catillus, commander of Evander’s army, founded Tibur.¹⁰⁴ Parthenope got its name from the tomb of a Siren by that name. It is now called Naples. Praeneste was founded by Praeneste, the grandson of Odysseus. Some authorities prefer to consider Caeculus as the founder, who, they say, was an offspring of the flames.¹⁰⁵ Diomedes founded Arpi and Beneventum; Antenor, Patavium; and the Pylians, Metapontum. However, I am not really interested in investigating the origins of cities.¹⁰⁶ → lat [643] Now, since the boundary of a continent is determined by the limitations imposed by intervening seas and straits, it is not inappropriate here to call attention to the lands, particularly the memorable ones, that emerge from the waters; these, because they are in the salt water, are called islands.¹⁰⁷ A concise survey ought not to be tedious.¹⁰⁸ So, in passing, I will mention the Pityussae, so called from their pine forests,¹⁰⁹ and now called Ebusus, in the vicinity of Cartagena; two Balearic Islands, Colubraria, and the islands which the Greeks call Gymnasiae;¹¹⁰ there is also Capraria, treacherous to ships. Off the coast of Gaul, near the mouth of the Rhone, is the isle of Metina; then comes an island called Blascon; next are three islands which are called Stocchadcs [lit., Islands in a Row]: they are /239/ known as First Island, Middle or Pomponiana Island, and Hypaea; then there are other small islands opposite Antipolis. → lat [644] In the Ligurian Sea is the island of Corsica, which the Greeks call Cyrnos. It is one hundred and fifty miles long and fifty miles wide. Its circumference extends three hundred and twenty-five miles. It has thirty-three states. The island of Elba is on the mainland side, and Oglasa below it. Sixty miles from Corsica is Planasia, treacherous to sailors, who are deceived in approaching it.¹¹¹ Then there are Urgo and Capraria, the Greek name for which is Aegilion; then Egilium, Dianium, Columbaria, and Veneria. Then beyond the Tiber mouth, in the vicinity of Antium, are Palmaria and Sinonia; and off the shore of Formiae are Pontiae, Pandataria, Prochyta, Abacneria, called by the Greeks Inarime;¹¹² and, in the vicinity of Naples, Pithecusa and Megaris. Eight miles from Sorrento is Capri; then comes Leucothea.¹¹³ → lat [645] Sardinia, facing the African Sea, is eight miles from Corsica. In the narrow strait there are small islands, which are called the Cuniculariae [Rabbit Islands];¹¹⁴ besides these there are Phinton and Fossa. Sardinia, named after Sardus, the son of Hercules, has the shape of a human foot. Indeed, it was called Sandaliotis and Ichnusa, both words suggesting the shape of a footprint. On the cast coast the island extends one hundred and eighty-eight miles; on the west one hundred and seventy-five; on the south seventy-seven; and on the north one hundred and twenty-five. Off the Gorditanum promontory there are two islands, called the Islands of Hercules; off Sulci¹¹⁵ the island of Enusis; and off the Caralis promontory the islands of Ficaria and Galata. Some authorities say that the Balaridac Islands, Gallode,¹¹⁶ and the Islands of the Baths of Hera are not far distant. Across from Paestum is Leucasia, which gets its name from /240/ a Siren buried there. Across from Velia are the Ocnotrides Islands, and opposite Vibo are the Ithacan Islands, which got their name from the watchtower of Odysseus.¹¹⁷ → lat [646] Next we must mention Sicily, which is called Sicania by Thucydides, and by many writers Trinacria. King Sicanus gave his name to the islands; he came there with a band of Spaniards before the Trojan War.¹¹⁸ Next came Siculus, the son of Neptune, who changed the name of the island to his. It is called Trinacria for the reason that, with its three projections, it is regarded as triangular: the Pachynus promontory faces south, toward the Peloponnesus, and is four hundred and forty miles from Greece; the Pelorus promontory faces westward¹¹⁹ and Italy, which is separated from it by a strait one and a half miles wide. Lilybaeum faces Africa and is one hundred and eighty miles distant from it. The distances between these capes, by overland measurement, are as follows: from Pelorus to Pachynus one hundred and seventy-six miles; from Pachynus to Lilybaeum two hundred miles; and from Lilybaeum to Pelorus one hundred and forty-three miles. → lat [647] There are five colonies in Sicily and sixty-three cities, many rivers and springs, and the awe-inspiring sight of Mount Aetna, spewing forth flames every night. Its crater measures twenty stadia;¹²⁰ it showers Tauromenium and Catana with hot ash, bellowing in loud uproar and thunderous crashings as the flames toss about.

→ lat [648] There are islands in the Sicilian Sea, too, to be sure. On the African side, Gaulos and Malta, lying at a distance of eightyeight miles from Camarina and one hundred and thirteen miles from Lilybaeum; Cossyra, Hieronnesos, Caene, Lampadusa, Astusa (called by some writers Aegusa), and still other islands. On the Italian side there are the following islands: opposite the Metaurus River, at a distance of 25 miles from Italy, are the seven Aeolian Islands, called the Hcphaestiades by the Greeks and Vulcan's Islands by us. These islands have separate names: the first Lipara, the second Therasia, the third Strongyle, where Aeolus is said to have reigned and where he /241/ knew, from the flames and their smoke erupting in the vicinity, from which direction the wind was going to blow; as a matter of fact, the inhabitants of this locality today have the same premonition. The fourth island is Didyme, the fifth Erephusa, and the sixth Phoenicusa, and the last Euonymus.

→ lat [649] The first European gulf of the Ausonian Sea¹²¹ extends ninety-six miles, and has three bays. The fore part of Italy, which is called Magna Graecia, begins here; it has an abundance of streams and towns. Then there is the port called Castra Hannibalis, at which point the breadth of Italy is a mere forty miles.

→ lat [650] The second gulf of Europe begins at the Lacinian promontory and, with a deep fold of coastline, terminates in the Acroceraunian promontory in Epirus; this point is eighty-five miles distant from the town of Crotona.¹²² From here Italy extends past many towns and bays, far into the sea, and reaches the city of Hydruntum, where the Lpper and Lower Seas are separated by nineteen miles;¹²³ at this point is found the shortest crossing into Greece. From here Italy continues past many peoples, bays, cities, rivers, mountains, and barbarian nations¹²⁴ to the territory of Illyricum, which extends, from the river Arsia to the Drina River, a distance of five hundred and five miles; and from the Drina to the Acroceraunian promontory, a distance of one hundred and seventy-five miles. The Illyrian coast has more than a thousand islands.

→ lat [651] The third gulf of Europe begins at the Acroceraunian Mountains and terminates at the Hellespont. It has nineteen bays¹²⁵ /242/ and many provinces. For there are Epirus, Acarnania, Aetolia, Phocis, Locris, Achaea, Messenia, Laconia, Argolis, Megaris, Attica, and Boeotia. Also, on the other side, on another sea, Phocis and Locris, Doris, Phthiotis, Thessaly, Magnesia, Macedonia, and Thrace – all of Greece.¹²⁶ Epirus begins at the Ceraunian Mountains. Here the first people are the Chaones, from whom Chaonia gets its name. Next comes Mount Pindus, the Dryopians, Molossians, and Dodoncans, famous for their celebrated oracle of Jupiter. Behind them, among other peoples, Moesia and Media border upon the Pontus; the Thracians extend to the Pontus. Presently the lofty peaks of Rhodope and Haemus are seen. Then come the colony of Buthrotum, and the Gulf of Ambracia, admitting the sea through narrow jaws; into it flows the Acheron River, famed in the legends of the underworld. Omitting several peoples, there is the colony of Actium, with its temple of Apollo, who has received an epithet from this place;¹²⁷ also the city of Nicopolis. Going from the Gulf of Ambracia into the Ionian Sea, we are confronted by various peoples, and then the Actolians, within whose borders, among other cities, is found close by the sea the city of Calydon, famous as the ancestral home of Diomedes and Tydeus.¹²⁸ Here an intervening gulf separates Aetolia and the Peloponnesus. In Acarnania there is Aracynthus; in Aetolia....¹²⁹ Then the Ozolae, with their town of Oeanthe, where the harbor of Apollo is located.¹³⁰ Next, in the plains of Phocis, are the town of Cirra, the harbor of Chaleon, from which, seven miles inland, is the town of Delphi, beneath Mount Parnassus, famous for the oracle of Apollo; the Castalian spring is located there. Then, in the deepest recess of the gulf, is the angle of Boeotia, near Mount Helicon.

→ lat [652] The Peloponnesus is a peninsula between the Aegean and /243/ Ionian seas, having deep inlets, with a perimeter of five hundred and sixty-three miles and, if the bays are measured, almost as much again. The narrow neck from which it protrudes is called the Isthmus. The opposing seas dash against it on either side, only five miles apart, and bite into the sides of the passageway. In the land between, which I have called the Isthmus, is the city of Corinth, sixty stadia from either shore, looking down upon both seas from a high elevation which is called Acrocorinthos. At the Isthmus begins a province called Achaia, formerly called Aegialos because of the cities located in a row along the coast.¹³¹ In this province are many bays, harbors, mountains, towns, and peoples.¹³² → lat [653] Hellas begins at the narrows of the Isthmus – the land which we call Greece. The first state in Greece is Attica, called Acte in antiquity. The part of it that borders on the Isthmus is called Megaris. On the coast is a harbor called ‘Scironian Rocks,’¹³³ six miles in length, with Athens set back from the sea by a wall five miles long.¹³⁴ There are many springs in Attica, of which a famous one is Callirhoe; and the springs of Boeotia are no less famous than those of Athens: they include Epicrene, Arethusa, Hippocrene, Aganippe, and Gargaphie.

→ lat [654] After many towns, mountains, and peoples we come to Haemonia, behind which is Mount Oeta.¹³⁵ This country is also known by the name Thessaly. Here was born a king by the name Graecus, who gave his name to the land of Greece; here also Hellen was born, from whom the Hellenes got their name. In Thessaly the most famous mountains are Pierian Olympus and Ossa, facing which are Pindus and Othrys, the abode of the Lapiths; these peaks /244/ look to the west; Mount Pelion looks to the east. All these mountains curve around, like a theater; before them lie seventy-five cities. Next to Thessaly is Magnesia, with its fountain Libethra, famed for its poetic inspiration.¹³⁶ The length of Thessaly is four hundred and ninety miles, and its breadth two hundred and ninety-seven miles.¹³⁷ → lat [655] Next comes Macedonia, a country of one hundred and fifty different peoples, and famous for outstanding kings; in particular Alexander; though it was believed that he was the son of Philip, his mother, Olympias, said that she had conceived him by a serpent. He was the conqueror of the world, for he had the same limits in his explorations and conquests as Bacchus and Hercules.¹³⁸ This country of Macedonia gave its name to the people who were formerly called Edonii, and to all of Mygdonia, Pieria, and Emathia. It extends as far as the borders of Thrace.¹³⁹ The southern part is inhabited by the Epirotes, the western by the Dardanians and the Illyrians; on the northern side is Paphlagonia and Paconia.¹⁴⁰ The boundary between Macedonia and Thrace is the Strymon River, flowing down the crest of Mount Haemus. In this range is Mount Rhodope, which they say is a Mygdonian mountain; then comes Athos, cut off from the mainland by Xerxes, who availed himself of his mighty Persian forces; and then the land of Orestis, undoubtedly getting its name from the son of Orestes and Hermione. Then comes Phlegra, now a town, famous for the reckless and monstrous battles of the giants.... This peak alone is said not to have been covered over in the deluge – to be sure, because of its preeminent elevation.¹⁴¹

/245/ → lat [656] Then comes Thrace, whose dull-witted inhabitants have the greatest yearning for death; the Bessi and the Denseletae live on the right bank of the Strymon,¹⁴² up to the Mesta River, which flows around the base of Mount Pangaeus. The snows of Odrysia fill the Hebrus River, which flows among various barbarian nations and also waters the lands of the Cicones, within whose borders is Mount Haemus, whose peak rises six miles¹⁴³ and is buffeted by winds because of its proximity to the stars. Behind it are found various nations, among them the Getae, the Sarmatians, and the Scythians. Next, the Sithonian people inhabit the area around the Pontus; their fame is derived from the genius of their poet Orpheus, who was born there; for his life on the Spertican promontory was devoted to either religious activity or the lyre.¹⁴⁴ → lat [657] Next comes the Maronian region and the town of Tyrida, in which the horses of Diomedes were stabled. Nearby is Abdera, to which the sister of Diomedes gave her name when it was built; this city is more celebrated as the birthplace of the natural philosopher Democritus. The poets have not overlooked the fact that Thrace is the burial place of Polydorus. There, too, is the promontory of the Golden Horn, famous for the city of Byzantium,¹⁴⁵ which is seven hundred and eleven miles distant from Dyrrhachium; that is the distance between the two seas, the Adriatic and the Propontis. At this point the Hellespont, narrowing to seven stadia, separates Europe from Asia. → lat [658] Here, too, are located two towns: one, Sestos, belonging to Europe; the other, Abydos, to Asia. Then there are facing promontories: Mastusia, on the Chersonesus, which marks the end of the third gulf of Europe; and Sigeum, in Asia, which is said to be the location of Cynossema, the tomb of /246/ Hecuba.¹⁴⁶ Not far off is the island of Tenedos, from which point the sea that lies between, as far as Chios, broadens out. On the right is Antandros. The smallness of the islands was frequently remarked upon by sailors, who compared them to a goat. Hence the Aegean got its name.¹⁴⁷ And on the Phalarian¹⁴⁸ promontory of Corcyra a rock resembles the form of a ship, into which [rock], according to ancient legend, the ship of Odysseus was changed.

→ lat [659] Crete, splendid with her hundred cities, stretches east and west. It got its name from a nymph, a beautiful daughter of Hesperis, or from Cretes, king of the Curetes. At first it was called Acria; subsequently Curetis; then it was called Isle of the Blessed because of its bland climate. In length it stretches two hundred and seventy miles; its breadth does not exceed fifty miles; its circumference extends five hundred and eighty-eight miles. Its highest peaks are Mounts Ida and Dictynna.

Euboea is separated from the mainland of Boeotia by so slight and narrow a current that it is linked in several places by bridges.¹⁴⁹ It is enhanced by two promontories: Geraestus, facing Attica; and Caphareus, facing the Hellespont. Its breadth ranges from two to forty miles. The length of the whole of Boeotia, froTn Attica to Thessaly, amounts to one hundred and fifty miles; its circumference is three hundred and sixty-five miles.¹⁵⁰ On this island are the cities of Chalcis, opposite Aulis, and Carystus, producing marble that is the color of the sea.

→ lat [660] In the Myrtoan Sea the Cyclades Islands get their name from their circular arrangement; of these the better-known are Delos and Antandros.¹⁵¹ Then, too, the Sporades Islands, of which Naxos /247/ is remembered for the tomb of Homer, and many other islands extend across seven hundred miles of longitude and two hundred miles of latitude. Between the Chersonesus and Samothrace are certain large and now barbaric¹⁵² habitats.

→ lat [661] The fourth of the great gulfs of Europe begins at the Hellespont and ends at the mouth of the Maeotis [Sea of Azov]. The sea between Europe and Asia is constricted and flows through narrows, seven stadia in width, called the Hellespont. Xerxes, king of Persia, collected his fleet, constructed a bridge, and led his army across here. These narrows extend along a channel for eighty-six miles;¹⁵³ then the sea becomes very broad and, soon again, it becomes constricted. The broadening of the sea is known as the Propontis, and the second narrows are called the Bosporus, one half mile in width. At this point Darius, the father of Xerxes, led his troops across by means of a bridge. The distance from the Hellespont is two hundred and thirty-nine miles.

→ lat [662] Next the Scythian bay of the broad sea¹⁵⁴ stretches out, at the middle of which is the Maeotis, joined by a narrow entrance; this inlet is called the Cimmerian Bosporus; it is two and a half miles wide. Between the two straits, the Cimmerian Bosporus and the Thracian Bosporus, is a distance of five hundred miles. The circumference of the entire Black Sea is two thousand one hundred and fifty miles, according to Varro, who says that the entire length of Europe is six thousand three hundred thirty-seven and a half miles. The Ister River rises in Germany, on the slopes of Mount Abnoba,¹⁵⁵ picking up sixty streams; it is also called the Danube.

→ lat [663] Beyond here extend the Scythian shores, a region densely populated with various barbarian races. Here are the Getae, the Dacians, Sarmatians, Amaxobians [Wagon-Dwellers], Troglodytes, /248/ Alani, and Germans. The entire stretch, from the Danube to the ocean,¹⁵⁶ is two thousand one hundred miles long, and in breadth four hundred miles, up to the wastes of Armenia.¹⁵⁷ Not far away are a river, a lake, and a town called by the same name, Borysthenes.¹⁵⁸ Nearby is the Isle of Achilles, famous, for his tomb. Inland live the Auchetae, in whose territories the Hypanis [Bug] River originates; and the Neuri, in whose territories the Borysthenes [Dnieper] begins. There are the Geloni, the Agathyrsi, the Man-Eaters, and behind them the Arimaspi, then the Rhipaean Mountains and a region covered over in darkling shadows.

→ lat [664] Behind these mountains and beyond the north wind are the Hyperboreans,¹⁵⁹ in whose vicinity the axis of the world continually rotates – a people remarkable for their customs, length of life, manner of worship, benignity of climate, six-month-long day, and their abode at the limit of human habitation. The region of Sarmatia, Scythia, and Taurica extends in length nine hundred eightyeight miles, and in breadth 710.¹⁶⁰ I am of the opinion that there is nothing to mention beyond here in Europe, since Asia has claimed even the Hyperboreans for itself.

→ lat [665] If, after crossing the Rhipaean Mountains, ysu go to the left, along the stretch of the northern Ocean, you will come a second time to the peoples of Germany, Gaul, Spain, and back to the Strait of Gibraltar. The Ariphaei, located in Asia, lead a life comparable to that of the Hyperboreans, and are admired by all races, so much so that people who are living in fear flee to their country to seek asylum.¹⁶¹ Beyond them are the Cimmerians and the Amazons, reaching as far as the Caspian Sea; this sea bursts into the Scythian /249/ Ocean near the place of the summer rising of the sun.¹⁶² After a long stretch of land we come upon Hyrcania.

→ lat [666] Then, returning to the shore of the Atlantic Ocean,¹⁶³ along the farther borders of Aquitania and Europe, we come to Britain. 1 his island lies to the north and the west, in length eight hundred miles, in breadth three hundred; the circumference is three thousand eight hundred and twenty-five miles. Nearby is the Caledonian Forest and very many islands, among which are the forty Orcades [Orkneys], almost joined together; then there are the Electrides [Frisian Islands], on which amber is found. The last of all the islands is Thule,¹⁶⁴ on which, at the summer solstice, there is continual daylight, and, at the winter solstice, continual night. At one day’s sailing beyond this island the sea is frozen over. Below Britain is the territory of Gaul and Spain. Were it not for the incursion of the Atlantic Ocean, Spain would be joined to Africa. For the town of Belon in Baetica is only thirty-three miles distant from Tingi,¹⁶⁵ which is a colony in Mauretania. Antaeus is said to have been the founder of this town.

→ lat [667] Africa and Libya got their names from Afrus, the son of the Libyan Hercules. In this region is the colony of Lissos. This is the site of the palace of Antaeus and of his famous wrestling match with Hercules; here are located the Gardens of the Hesperides. Here also is the winding estuary which the ancients sportively referred to as a guardian serpent. Not far away is Mount Atlas, raising its peak from the bosom of the sands. The natives call it Mount Addiris.¹⁶⁶ It rises up to the vicinity of the moon’s orbit, above and /250/ beyond the forces of the clouds. The western side faces the shores of Oceanus; it is thickly wooded, teeming with springs, but infertile because of its rocks. But the side that faces the province of Africa is all luxuriant. It grows trees that look like cypresses but have an oppressive odor; these produce a precious fleece, like that of silk. By day the mountain is silent, but at night there is a flashing of fires and a commotion of flutes and pipes, cymbals and drums, and of frenzied Satyrs and Goat-Pans.¹⁶⁷ → lat [668] Beyond it, toward the west, for a distance of four hundred and ninety-six miles, stretches a forest filled with wild African animals. Not far distant are seven mountains which, because of their equal height, are called ‘The Brothers’; they are teeming with elephants, and lie beyond the province of Tingitana, whose length is one hundred and seventy miles.¹⁶⁸ Then there is the town of Siga, the royal residence of Syphax, facing the city of Malaga in Spain. Along the coast is Cartcnna, and the larger town of Caesarea; then Icosium, with no less favorable political status; then Rusguniae and Rusuccurru, Saldac, and other towns, Igilgili and Tubusuptu. The river Ampsaga is three hundred and twenty-two miles distant from Caesarea. → lat [669] The length of the two Maurctanias is one thousand and thirty-eight miles, the breadth four hundred and sixty-seven miles.

Numidia, famous for its association with Masinissa, begins at the Ampsaga River. Its name is derived from the Nomads. Inland is the colony of Cirta, and further inland are Sicca and Bulla Regia. Along the coast are Hippo Regius and Thabraca; inland is the district of Zeugitana, properly called Africa. It has three promontories: Candidum; Apollo, facing Sardinia; and Mercury, facing Sicily. Projecting into the sea, they form two bays, beginning at Hippo Diarrhytus. Then comes the promontory of Apollo; and, on the next bay, Utica, remembered as the place of Cato’s death; the river Bagradas; and, nearby, Carthage, once famous in war, now awesome /251/ in her prosperity.¹⁶⁹ Finally there are Maxula, Carpis, Missua, and Clupea, on the promontory of Mercury; then Curubis and Neapolis.¹⁷⁰ → lat [670] Then come those, called Libyphoenicians, who inhabit Byzacium, a region whose circumference measures two hundred and fifty miles and whose sowings are repaid by hundredfold harvests. Here are the towns of Putput, Hadrumetum, Leptis, Ruspae, Thapsus, Thaenae, Aves, Macomades, Tacape, and Sabrata, on the fringe of the Syrtis Minor. To this point from the Ampsaga River the length of Numidia and Africa is five hundred and eighty miles, the breadth two hundred miles.

→ lat [671] The third gulf is divided into the two bays of the two Syrtes with shallow tidal waters. Syrtis Minor is three hundred miles distant from Carthage. The journey to the Syrtis Major is through deserted regions that are infested with various kinds of serpents and wild beasts. Next come the Garamantes; beyond them the Psylli once lived. Along the recessed coast are the municipalities of Oea and Leptis Magna; then comes Syrtis Major, which measures six hundred and twenty-five miles around.

→ lat [672] Next is Cyrenaica, also called Pentapolis, famous for the oracle of Jupiter Ammon, which is four hundred miles from Cyrene. There are five leading cities here: Berenice, Arsinoe, Ptolemeis, Apollonia, and Cyrene. Berenice [Benghazi] is on one end of the horn of the Syrtis; here are the Gardens of the Hesperides,¹⁷¹ the river Lcton, and a sacred grove; the distance from Berenice to Leptis is three hundred and seventy-five miles. Arsinoe is forty-three miles away from Leptis; and next comes Ptolemais [Barce], twenty-two miles farther on. Far distant are Catabathmos and the Marmaridae and, along the shore of Syrtis, the Nasamones; then Mareotis; then a locality in Egypt, Apis, which is sixty-two miles from Paraetonium; from there to Alexandria is two hundred miles. The length of all /252/ Africa from the Atlantic Ocean, including Lower Egypt, is three thousand and forty miles; from the ocean to Greater Carthage is one thousand one hundred miles; from it [Greater Carthage] to Canopus, the nearest mouth of the Nile is one thousand six hundred and eighty-eight miles.

→ lat [673] The interior of Africa faces south, with deserts intervening, and is the abode of the White Ethiopians, the Nigritac, and other peoples of monstrous strangeness. After these, to the cast, are appalling wastelands. The river of this region is the Niger, of the same nature as the Nile. The Atlantes dwell amidst these wastes; they possess no names and curse the sun because it scorches them and their crops relentlessly. These people seem never to have dreams.

→ lat [674] The Troglodytes live in caves, and feed upon serpents, and hiss instead of speaking. The Garamantes generally consort with women without marrying them. The Augilae worship the powers of the underworld. The Gamphasantes are naked and unwarlike, and never mingle with outside peoples. The Blemmyac have no heads and have their mouth and eyes in the chest. The Satyrs have nothing human except their faces. The Goat-Pans are as they are represented in paintings. The Strap-Feet, because of a disability of their feet, crawl rather than walk.¹⁷² The Pharusi were companions of Hercules. These people mark the end of Africa.

→ lat [675] After this comes Egypt, which is the beginning of Asia. This land measures two thousand six hundred and thirty-eight miles from the Canopic mouth of the Nile to the entrance to the Black Sea; and from the entrance to the Black Sea to the entrance to the Maeotis, one thousand six hundred and seventy-five miles. The interior of Egypt stretches southward as far as the Ethiopians, who border it in the rear. Lower Egypt is embraced by the Nile, which divides on the left and the right, so that you might refer to Egypt as an island of the Nile; for the circumambient river is thought to mark off the delta, too, in the shape of the letter delta. From the point of its division, to the Canopic mouth, is a distance of one hundred and forty-six miles.

/253/ → lat [676] The upper part of Egypt, bordering upon Ethiopia, has many prefectures of towns, called nomes: among them are Menelaite, the district of Alexandria, and Mareotis of Libya. Heracleopolis is an island of the Nile, on which are the towns of Hercules, Arsinoitc, and Memphite,¹⁷³ which extend to the apex of the delta. The sources of the Nile itself are believed to be undetermined, although King Juba¹⁷⁴ points out that it rises on a mountain of lower Mauretania, on a lake of the Nile – a theory that is substantiated by the animals there, and their method of reproduction, resembling those of other parts of the Nile. The entire delta area once contained two hundred fifty towns, according to Artemidorus. On the seacoast of Egypt lies Alexandria, one of the more illustrious cities, founded by Alexander the Great – twelve miles from the Canopic mouth, and bordering upon Lake Mareotis, which has many islands and four hundred crossings.¹⁷⁵ Its length, as well as its breadth, is one hundred and fifty miles.

→ lat [677] Beyond the Pelusiae mouth is Arabia, stretching to the Red Sea, which is also called the Erythraean Sea, from King Erythras, the son of Perseus and Andromeda; the name Red Sea comes from its color.¹⁷⁶ There is a spring along the shore which causes sheep, where they drink of it, to begin to change the color of their wool to a reddish hue. Arsinoe is a town on this sea. → lat [678] Arabia extends as far as the perfume-bearing and opulent land.¹⁷⁷

The country next to it is Syria, delimited under many names. For it is Palestine where it borders upon Arabia; and Judaea and Phoenicia; the part inland is called Damascene; extending to the south, Babylonia and also Mesopotamia, between the 1 igris and Euphrates rivers; where it crosses the Taurus Mountains, Sophcne; on this side of Sophcne it is called Commagene; and, on the other side of Armenia, Adiabene, which was formerly called Assyria; and where it borders upon Cilicia, Antiochia. The length between /254/ Cilicia and¹⁷⁸ Arabia is four hundred miles, and the breadth, from Sclcucia to the town of Zeugma on the Euphrates, is one hundred and seventy-five miles.

→ lat [679] Arabia begins at Ostracina, sixty-six miles from Pelusium. Next comes Apollonia, advancing along one hundred and eightyeight miles of Palestine.¹⁷⁹ Across from Idumaea and Samaria, Judaea extends far and wide. The part of it that borders upon Syria is called Galilee, separated from the rest by the river Jordan,¹⁸⁰ which originates in the spring of Paneas....’¹⁸¹ the second elevation of Judaea from Jerusalem; on the same side is the spring of Callirrhoe. On the west are the Essencs, who live without indulging in intercourse or any other pleasures. Somewhat farther inland is the fort of Masada, marking the border of Judaea. Decapolis is just across the border, getting its name from the number of its towns. → lat [680] As we return along the shore of Phoenicia, there is the colony of Ptolemais. Behind Phoenicia are the Libanus and Antilibanus mountains, and in the intervening plains Mount Bargylus is situated. As Syria comes to an end, amidst the towns of Phoenicia,¹⁸² there is Antioch, which is split by the Orontes River. Above it rises Mount Casius, from whose heights the sun is visible through the darkness at the fourth watch of the night.¹⁸³ → lat [681] The Euphrates River rises in Syria on a mountain called Capotes. There is also another stream, called the Marsyas. Between Syria and Parthia is the city of Palmyra,¹⁸⁴ and presently the Euphrates River. By a ten days’ sail along this river, one reaches Seleucia, the chief city of the Parthians. The Euphrates River splits, flowing to the left into Mesopotamia and pouring into the Tigris; the right-hand /255/ course makes its way to Babylonia, which is the capital of Chaldea.¹⁸⁵ → lat [682] We must now return to the coast of Syria, bordering upon which is Cilicia; here are located the town of Venus, the island of Cyprus, and the river Paradisus.¹⁸⁶ Cilicia is joined to Pamphylia, the last town of which is Phaselis. Next comes Lycaonia, assigned to the jurisdiction of Asia; on that side where it borders on Galatia, it has fourteen towns. → lat [683] Lycia borders upon Pamphylia. Here the Taurus range begins, looking down upon almost half of the world, which it would run through continuously if the seas did not stand against it.¹⁸⁷ Swerving somewhat, it passes alongside, and under various names it makes its way to the peaks of the Rhipaean Mountains; for, among other names, it is called the Niphates, the Caucasus, or the Sarpedon; it is also known as The Gates, in one place the Armenian Gates, in another the Caspian Gates...; still other names of the mountains are the Hyrcanian,¹⁸⁸ the Coraxian, the Scythian, and the Ccraunian.

→ lat [684] In Lycia there is another mountain, Chimaera, which flashes with fires at night. Lycia once had seventy towns; now it has thirty-six. It comes to an end at a town called Telmesus. Here begins the Asiatic or Carpathian Sea and the province which is properly called Asia. To the east of it are Phrygia and Lycaonia, to the north Paphlagonia. The length of this province is four hundred and seventy miles, and the breadth three hundred miles. The other part¹⁸⁹ is bounded by Armenia on the cast and Pontus on the north.

→ lat [685] Nearby is Caria; then comes Ionia and beyond it Aeolis. In Phrygia is the town formerly called Celaenae, the name now /256/ changed to Apamea. Marsyas was born and died there; he gave his name to the river and competed with Apollo. That part of the river is called the Aulocrenc,¹⁹⁰ from which the Maeander River originates. → lat [686] Phrygia looms above the Troad; on the north is Galatia; on the south it borders upon Lycaonia,¹⁹¹ Pisidia, and Mygdonia; on the cast it borders upon Lycia; on the north Mysia and Caria. Then comes Mount Tmolus, abounding in saffron, and the Pactolus River. Milctos is the capital of Ionia; there is also located Colophon, famous for the oracle of Apollo Clarius. The chief city of Maeonia is Sipylus;¹⁹² then Smyrna, best remembered for Homer;¹⁹³ around it the Meles River flows. The Hermus River cuts through the Smyrnaean plains, rising at Dorylaus, and dividing Phrygia from Caria. Near Ilium is the tomb of Memnon. Inland, above the Troad, is Tcuthrania, which once was the district of the Moesi;¹⁹⁴ the town of Tcuthrana is washed by the Caicus River. Among all the cities of Asia, Pergamum is the most famous.

→ lat [687] Bithynia marks the beginning of Pontus, and on the cast, facing Thrace, it has its first inhabitants at the Sagaris River.¹⁹⁵ This river joins with another river, called the Gallus, from which the Galli, the priests of the Great Mother,¹⁹⁶ get their narfle. Bithynia, named after its king Bithynus, was also called Bebrycia and Mygdonia. In it is the city of Prusias, which Lake Hylas inundates; here the boy by the same name is said to have been overtaken.¹⁹⁷ /257/ Here also is the place Libyssa, near Nicomedia, where the tomb of Hannibal is said to be located. → lat [688] Next comes the shore of Pontus. After the mouth of the Bosporus and the Rhesus and Sagaris rivers comes the bay of Mariandynus,¹⁹⁸ on which are found the town of Heraclea and the harbor of Aconae, where the poisonous herb aconite grows; and the Achcrusian cavern, which plunges into the depths of the earth.

→ lat [689] Next comes Paphlagonia, and behind it is Galatia. Here also is the town of Enetosa,¹⁹⁹ from whose citizens it is asserted that the Veneti in Italy were descended. There is the cape of Carambis, two hundred and twenty miles from the mouth of the Black Sea, and the same distance from the entrance of the Sea of Azov. There are also Mount Cytorus and the town of Eupatoria, founded by Mithridates; but after his defeat, its name was changed to Pompeiopolis.²⁰⁰ → lat [690] Cappadocia recedes into the interior, running past both [Greater and Lesser] Armenias and Commagene on the left, and past many peoples of Asia on the right. It rises in the east toward the ridges of the Taurus Mountains, passes Lycaonia, Pisidia, and Cilicia, and going beyond the expanse of Syria Antiochia, it extends partly into Scythia.²⁰¹ Cappadocia is separated from Greater Armenia by the Euphrates River. Armenia begins at the Panedri Mountains. In Cappadocia there are many notable cities, among them Melita, founded by Semiramis, and Mazaca, called the mother of cities. It is located beneath Mount Argaeus, on whose white peak the snow does not melt even in the summer heat. On this side of Cappadocia the length of Asia is one thousand one hundred and forty miles.

/258/ → lat [691] Assyria begins at Adiabene;²⁰² Media comes next, facing the Caspian Sea, which is girt by the Caucasus Mountains. The Caucasus has gates, which are called the Caspian Gates – abrupt cliffs further barred by iron beams to prevent outside peoples from passing through; in addition, the passage is blocked in the. springtime by serpents.²⁰³ The distance from the Gates to the Black Sea is known to be two hundred miles. The Symplegades Islands are in the Black Sea; next comes Margiana, the only vine-bearing region in that area, shut in by mountains of one thousand five hundred stadia, hard to reach because of the sandy wastelands which extend one hundred and twenty miles. Alexander the Great was attracted by the delightfulness of this region, and founded there the first city named after himself. Subsequently destroyed, it was later rebuilt by Antiochus, son of Seleucus, and given the name of his father.²⁰⁴ The city is seventy-five stadia in circumference. → lat [692] Then comes the Oxus [Amu Darya] River, which flows around Bactra, with a town and a river of this name.²⁰⁵ Beyond that is Panda, a town of the Sogdiani, where Alexander founded his third Alexandria, as a memorial to the long extent of his journey; indeed, altars were set up there by Dionysus, then by Hercules, to bear witness to their immense labors in traversing those regions. The Laxates [laxartes, Syr Darya] River cuts through that part of the world, a river which formerly was presumed to be the Tanais [Don]. But the general Dcmodamas crossed the river and pointed out that the two were not the same; and beyond he set up an altar to Didymaean Apollo.

→ lat [693] The Persians and the Scythians have a common border. At the Scythian Ocean and the Caspian Sea, as our course goes toward the eastern Ocean, there are deep snows at first and then a long desert, beyond which the Man-Eaters make passage impossible. Still /259/ farther in are the Chinese, who drench their trees with water, so that the fleece which produces silk can be gathered. The Chinese shun contacts with other nations, but they delight in negotiating a transaction by laying out their wares without exchange of words.²⁰⁶ Then comes Attacenus Bay, rivaling the land of the Hyperboreans in its blissfulness; here the inhabitants take great joy in the fact that because of the curving of their valleys they suffer from no pestilential winds.²⁰⁷ → lat [694] Next comes India. A mistaken notion²⁰⁸ has placed the Cicones in between. India begins with the Medi Mountains.²⁰⁹ Stretching southward to the eastern Ocean, it is a healthy land because of the invigorating breezes of Favonius; its soil is enlivened by a second summer each year, and it produces two crops; instead of winter it suffers from etesian winds. India had five thousand towns²¹⁰ and was believed to be a third part of the world. Dionysus was the first to make his way into India and celebrate a triumph. The largest rivers in it are the Indus and the Ganges. The Ganges comes down from the Scythian Mountains. The Hypanis River is there, a raging stream which brought the march of Alexander to a halt, as the altars on its banks bear witness. The breadth of the Ganges at its widest extent is twenty miles, at its narrow point eight miles; its depth is one hundred feet. Kings rule in India, and there is a great diversity of nations and an abundance of armies and elephants. Beyond the city of Palibothra is Mount Maleus, where the shadows in winter fall to the north and in summer to the south, alternating every six months. In this locality Ursa Major is visible for only fifteen days a year. → lat [695] The men are dark-skinned. Pygmies live in the mountainous regions; those who border on the ocean get along without kings. Women hold sway over the Pandaean race; /260/ their former queen was a daughter of Hercules. In this region is also found the city of Nysa, sacred to Dionysus, and Mount Merus, sacred to Jupiter; whence the story originated that Dionysus sprang from the thigh of Jupiter.²¹¹ There are also two islands remarkable for their mineral deposits and production of silver and gold; this is borne out by their names, for one is called ‘Golden Island,’ the other ‘Silver island.’ → lat [696] All Indians beautify themselves by dyeing their hair; some with bluish, others with yellowish, dyes; they adorn themselves with jewels; they give little thought to funerals, and consider it a distinction to ride on elephants.²¹²

On the island of Ceylon the elephants are larger than the Indian elephants; and the pearls are larger. This island extends seven thousand stadia in length and five thousand in breadth. It is divided by a river, and it stretches along the side of India; the journey takes seven days, as has been proved by Roman sailors. The sea there, apart from deep channels, is six paces in depth.²¹³ Ursa Major is not visible there, nor are the Pleiades ever seen; the moon is visible only from the eighth to the sixteenth day of each month. → lat [697] The brightest star there is Canopus; the sun rises on the left-hand side.²¹⁴ Sailors do not observe the stars in sailing, and instead follow the flight of birds, which they carry on board. They navigate during only four months of the year. The men there are larger than any humans, have reddish hair, blue eyes, and harsh-sounding voices; they have no oral dealings with other people. They come to a river bank with foreign tradesmen and lay down their wares and make an exchange as soon as it is agreeable.²¹⁵ Their span of life is abnormally /261/ long, so that a man who dies at the age of one hundred, is not long-lived. They do not sleep in the daytime. The cost of grain does not fluctuate. Their buildings are small and insignificant. They have no knowledge of the vine, but they have plenty of fruits.

→ lat [698] They worship Hercules. They select as their king a man who is gentle, elderly, and childless; if he has offspring during his reign, they depose him, because of their fear of hereditary rule. Thirty others hear a court case with him, and if there is an appeal seventy judges are appointed.²¹⁶ The king is dressed in the manner of Dionysus; and if he commits a sin he is cut off from all communication and conversation, and has his throat cut. They love to till the soil and to go hunting – that is, on tiger- and elephant-hunts. They delight in fishing, especially for turtles, whose shells they use to cover their large houses.²¹⁷ → lat [699] Next come the Fish-Eaters, whom Alexander forbade to eat fish. Not far away is the Island of the Sun, so called, and the red ‘Couch of the Nymphs,’ where all animals die because of the intensity of the heat.²¹⁸ Then the Hypanis River²¹⁹ of Carmania, where Ursa Major first becomes visible. Then there are three islands where sea serpents are found twenty cubits long. Along these shores the Red Sea is parted in two gulfs; the eastern one is called the Persian Gulf, after the inhabitants there; this gulf measures two thousand and sixty miles in circuit; the other gulf, across from it, is called the Arabian Gulf.

→ lat [700] Persia borders upon Carmania, beginning at the island of Aphrodisias; it changed its name to Parthia. The shore, which faces west, is five hundred and fifty miles long. A famous city there is Susa, in which is located the temple of Diana of Susa. Carbyle or Barbita is one hundred and thirty miles away; there are men there who bury gold deep in the ground, to keep anyone from using it. The Parthian kingdom extends nine hundred and forty-four miles. /262/ Media, Parthia, and Persia, taken together, are bounded on the cast by the Indus River, on the west by the Tigris, on the north by the Caucasian Taurus range, and on the south by the Red Sea. Together they extend one thousand three hundred and twenty miles in length and eight hundred and thirty miles in breadth.

→ lat [701] Babylonia²²⁰ is the capital of the Chaldacan people; in fact, Assyria and Mesopotamia, because of the fame of that city, are known as Babylonia. The city itself is surrounded by walls sixty miles in extent, two hundred feet high, and fifty feet wide, or even more; for the Babylonian foot is three inches longer than our measure. The city is washed by the Euphrates River. The temple of Jupiter Belus, who was the discoverer of the science of the stars, is here. This city has now gone back to desert waste, its population drained by nearby Seleucia. For this very purpose the Parthians founded Ctesiphon, three miles from it; and Ctesiphon is now the capital of the kingdoms.

→ lat [702] The remote and scorched portions of Ethiopia are inhabited by Troglodytes and Fish-Eaters; the former surpass wild beasts in speed of foot, the latter swim faster than the creatures of the sea.²²¹ The Gorgades Islands are opposite a promontory which is called the Horn of Hesperus. It is reported that the Gorgons lived there, two days’ sail from the mainland. Beyond these are the Isles of the Hesperides, which are far out to sea. There is no doubt that the Isles of the Blessed are situated to the left of Mauretania, toward the southwest. The first of these is called Membronia,²²² the second Junonia, the third Theode,²²³ the fourth Capraria; and still another, Nivaria,²²⁴ with a cloudy and frosty sky. Next come the Canary Islands, full of dogs of an immense size. All the islands are filled with birds and are heavily wooded with palms and conifers, abounding in honey, streams, and sheatfish.

→ lat [703] In my brief survey of the regions of the world, I could /263/ not tarry, and I skipped over those areas that are insignificant; nevertheless, so that it will be appreciated that I have traversed the entire sweep of lands and seas, I shall briefly indicate the total dimensions. The longitudinal distance, by direct route, from the Strait of Gibraltar to the mouth of the Sea of Azov, is 3,437 miles. The entire circuit, starting at the same point and measured along the bays that have been listed above, is 15,700 miles, and, with the addition of the Sea of Azov, 18,290 miles. The measurement of Europe alone is 8,294 miles. The length of Africa is 3,794 miles; the breadth, going into the Cyrenaic region, is 910 miles. The length of Asia is 6,375 miles; the breadth, from the Ethiopian Ocean to Alexandria on the Nile, measured through Meroe and Svene, is 1,825 miles.²²⁵ I have set forth the dimensions of the lands and the seas which I have traversed. Now, in accordance with your request, I shall come to the subject matter of the discipline of geometry."

→ lat [705] At these words Mirth was aroused by the maidservants of Venus, and joked with Venus herself (who was close by), but in soft and restrained tones. Mercury, with the good-humored nod with which he usually regarded Venus, cautiously checked her, for fear /264/ of rebuke from the gods. But Juno Pronuba,²²⁷ seated near, said: “It is not at all strange that Venus is readily inclined to play the wanton with such a jovial company of favorites and attendants; for she is always gay at weddings and charming when Mercury smiles at her.”

At this point Geometry was ordered to get on with the subject she had promised, but to touch lightly on the main points of the discipline, so as not to vex her audience with her protracted discourse.²²⁸ → lat [706] She then spoke out:

“Every affirmation that I make which extends to infinity is distinguished by numbers or lines, which are acknowledged to be either corporeal or incorporeal. For the one we apprehend solely by our intellects, and the other we apprehend by sight. The first class, which arises from the rules and reckonings of numbers, is assigned to my sister Arithmetic. The second class is the linear and demonstrable knowledge drawn from this dust;²²⁹ begotten indeed from incorporealities, and fashioned into manifold perceptible shapes from a slight and scarcely comprehensible beginning, it is elevated even into the heavens.²³⁰ → lat [707] That which is incorporeal and an invisible first beginning is shared in common by me and my sister Arithmetic. Her indivisible monad is the begetter of numbers; with me it is referred to as a mark or point because, being that it is not apprehensible, it is not divided into parts; with her the dyad produces a line; for me a line is that which is produced in length, but takes on nothing of breadth. Moreover, a surface with me extends in length and breadth but is thought of as having no depth; with her, number, which is able to refer to all figures, in groups or singly, is found to be incorporeal, unless it is applied to objects. And so the beginnings that belong to both of us are incorporeal.²³¹

/265/ → lat [708] In my discipline there are two primary categories of figures: one, which is called plane, epipedon in Greek; the other solid, in Greek stereon. The beginning of the first type is called semeion in Greek; we call it a point (punctum) or mark (signum) in Latin; the beginning of the second type is a surface, called epiphaneia in Greek. A point is that whose part is nothing.²³² If there be two points, they are joined by a connecting line.²³³ The line (as we call the Greek grammē) is length without breadth.²³⁴ → lat [709] Some lines are straight, eutheiai in Greek; others are curved into circles, kyklikai; others I classify according to their deviation as spiral, helikoedeis in Greek, and still others as curved, kampulai in Greek.²³⁵ These lines terminate in points at either extremity, just as the lines themselves bound surfaces. A surface has only length /266/ and breadth,²³⁶ and lacks depth, as is the case with color on a body. The Greek name for surface is epiphaneia and, as I have said, the extremities of a surface, whether it be plane or curved, are lines.²³⁷ → lat [710] A plane angle is formed on a surface by two lines meeting one another and making not one inclination to each other.²³⁸ When the lines that contain an angle are straight, the angle is called rectilineal,²³⁹ or in Greek euthygrammos. When a straight line stands upon another straight line and forms equal angles to the right and left, each of the angles is called a right angle, and the line that stands above is called a perpendicular, or in Greek kathetos.²⁴⁰ An angle greater than a right angle is called an obtuse angle,²⁴¹ and one less than a right angle, an acute angle.²⁴² A boundary is that which is an extremity of anything.²⁴³ A figure is that which is contained by any boundary or boundaries.²⁴⁴ → lat [711] A circle is a plane figure which is contained by one line; the line is called a periphery, to which, from one point lying within the circle, all straight lines are drawn equal.²⁴⁵ The middle point of the circle is the center.²⁴⁶ A diameter is any straight line, drawn through the center, which divides the circle into equal parts.²⁴⁷ A semicircle is the figure which is contained by the diameter and the half-circumference /267/ which that same diameter cuts off.²⁴⁸ Three straight lines lying in different directions form a triangle, four, a tetragon; and many, a polygon.

These are called plane figures, of which there are three kinds: the first is contained by straight lines, and is called by the Greeks euthygrammos; the second is contained by curved lines, and they call it kampulogrammos; the third, which is fashioned from both straight and curved lines, they call a mixed (mixton) figure.²⁴⁹

→ lat [712] Rectilinear figures are called trilateral, quadrilateral, or multilateral.²⁵⁰ A trilateral figure has three forms: a triangle is either equilateral, having three sides of equal length; or isosceles, having two of its three sides of equal length – two equal legs, as it were, and hence it is called ‘equal-legged’; or scalene, having three sides of unequal length.²⁵¹ Quadrilateral figures have five different forms: first, the square is contained by four straight lines of equal length and is right-angled; the second is right-angled but not equilateral, and is called oblong; the third is equilateral but not right-angled, and is called a rhombus; a figure that has its opposite sides and angles equal to one another and yet does not have equal sides nor right angles is called a rhomboid; and any other quadrilateral figure not having one of these forms is called a trapezium.²⁵² Parallel lines are straight lines which lie in the same plane and, if produced to infinity, never meet.²⁵³ Our discussion has been concerned with quadrilateral figures whose resemblance to multilateral figures can teach us about the latter. These include pentagons, hexagons, and others of a rectilineal nature.

→ lat [713] Next comes the second kind of figures, those that are formed by curved lines; the Greek name for these figures is kampulogrammos. They are of two types: the first deals with propositions involving perfect circles. Now a circle is ‘perfect’ if all lines produced to its circumference from a central point, in all directions, are of equal length. The second type shows the different kinds of /268/ elliptical figures. → lat [714] Then there is a third kind of plane figures, which is called ‘mixed’: these figures are contained partly by curved lines and partly by straight lines, as in the case of a semicircle, whose curved line forms the circular part and whose straight line, as I have said, is called the diameter, or distermina in Latin, if the diameter is found in a complete circle, it extends through its center to the circumference on either side.

→ lat [715] Of demonstrations involving these kinds of plane figures, some have to do with problems (ergastica), others with theorems (apodictica).²⁵⁴ Those that apply to problems contain instructions for constructing any sort of figure; those that apply to theorems present proofs of what the theorems state. The former class have Greek designations: first, tmēmatikos; second, sustatikos; third, anagraphos; fourth, engraphos; fifth, perigraphos; sixth, parembolikos; seventh, proseuretikos. Tmēmatikos deals with the steps involved in cutting off lines in the required manner. Sustatikos demonstrates the steps involved in joining given lines. Anagraphos is the term applying to the steps in describing a prescribed figure. Engraphos shows the steps by which we enclose a prescribed triangle or other figure within a given circle. Perigraphos is the term applying to the demonstration of circumscribing a given circle with a square or other figure. Parembolikos has to do with inscribing a given triangle within, for example, a given quadrilateral so that the spaces²⁵⁵ of the quadrilateral may increase without changing the figure. Proseuretikos is the term for finding, for instance – given two lines of unequal length – a third line which is as much smaller than one of the two lines as it is larger than the other. These are the general terms for figures applying to problems.²⁵⁶

→ lat [716] We may now touch lightly upon the terminology of figures applying to theorems, inasmuch as I have those in common with my sister, Dialectic, whom you have already heard. All these figures involve five steps, which are known by their Greek names: first, protasis; second, diorismos; third, kataskeuē; fourth, apodeixis; fifth /269/ sumperasma,²⁵⁷ We can explain these in Latin as follows: the first is the enunciation of the proposition (schematis propositum); the second is the definition (determinatio) of what is sought (questionis); the third is the construction (dispositio argumentorum); the fourth is the demonstration and proof (demonstratio, comprobatio); and the last is the conclusion (conclusio). So much for the classifications of plane figures. Now let us return to the components of theorems; to be sure, these components are lines and angles.

→ lat [717] Angles are of three different kinds: an angle is either upright, narrow, or broad. An upright angle is a right angle and is always the same; a narrow angle is an acute angle, and is always variable; a broad angle is an obtuse angle, and is likewise variable. For if an angle is broader than a right angle, whether much or slightly broader, it will still be obtuse; and when you change the degree of the angle, it remains in the same category, because its variability comes from the lines, when they form larger or smaller obtuse angles.

There are four terms that are used in proportions: first, isotes [equal]; second, homologos [corresponding]; third, analogos [analogous]; fourth, alogos [disproprotional]. The ratio is equal when two lines of equal length bear a double²⁵⁸ or equal²⁵⁹ relationship to a third line; a corresponding ratio, when the lines compared are in agreement; an analogous ratio, when the line that is half as long as another is twice as long as a third; and lines are disproportions when they are neither equal nor bear any other ratio – half, third, double, triple – to each other.²⁶⁰ → lat [718] All magnitudes are said to be commensurable or incommensurable. A magnitude is commensurable if it is the first to be considered or is commensurable with another line when they are /270/ measured by a common measure.²⁶¹ Whatever is proportional is said to be commensurable. A given line, though it has not been compared, nevertheless because it is still not incommensurable when compared with another and has something which, in itself and by itself, performs rationally, is called commensurable. A line becomes incommensurable if it does not have any common measure when compared with another line. → lat [719] Lines which are proportional to each other we call commensurable; and those that are not proportional, incommensurable. Measure is not alone responsible for commcnsurability; power also causes lines to be commensurable, and they are said to be ‘commensurable in power.’²⁶² Lines commensurable in measure are called commensurable. All lines that are commensurable neither in measure nor in power are called incommensurable.

→ lat [720] Of these there are thirteen irrational straight lines: the first is called medial; the second, binomial (which is divided into six species: first binomial, second binomial, third binomial, and so on); the third kind is called the first bimedial, and corresponding to the one above; the fourth is called the second bimedial; the fifth is called the major; the sixth is called ‘the side of a rational plus a medial area’; the seventh is called ‘the side of the sum of two medial areas’; the eighth is called the apotome, and there are six species of this (they are called first, second, third, and so on, as above); the ninth is called the first apotome of a medial straight line; the tenth, the second apotome of a medial straight line; the eleventh is called the minor; the twelfth is called ‘producing with a rational area a medial whole’; and the thirteenth is called ‘producing with a medial area a medial whole.’²⁶³ All these irrational lines, mingled with other lines, either bear their own virtues or receive those of others, and by various relationships demonstrate definite measures of space, which the Greeks call chōria [areas]. Let this suffice about plane figures.

→ lat [721] Now let us consider solid figures, which are called sterea. /271/ A solid is a figure which has length, breadth, and depth.²⁶⁴ Its extremities consist of surfaces,²⁶⁵ just as the extremities of surfaces consist of lines. Solid figures are based upon surfaces which are plane figures: a pyramid is imposed upon a triangle lying beneath; a cone or a cylinder upon a circle; a cube upon a square, and so on. → lat [722] The sphere, containing all other figures within itself, consists of circles into which it is resolved. Solidity brings into being the basic figures: those which the Greeks call pyramids; also the prism, the sections of which are similar; also, likewise, the cube, the cone, the cylinder, and the sphere. To these are added the ‘noble’ figures fashioned from them: the octahedron, the dodecahedron, and the icosahedron.²⁶⁶ To enable us to demonstrate these matters as a whole in proper order in the dust of our abacus, the following must be postulated at the start: from any point to any point to draw a straight line; to produce a finite straight line continuously in a straight line; to describe a circle with any center and any distance; that all right angles are equal to each other; to produce any finite straight line of any length; if a straight line falling on two straight lines should make the two interior angles on the same side less than two right angles, then the two straight lines meet on that side on which the angles are less than two right angles.²⁶⁷ → lat [723] There are three common notions: things which are equal to the same thing are equal to each other; if equals be added to equals, the wholes are equal; if equals be subtracted from equals, the remainders are equal.”²⁶⁸ → lat [724] When Geometry saw that these matters were accepted, /272/ she drew a straight line upon the abacus and asked: “How does one go about constructing an equilateral triangle upon a given finite straight line?" When the learned company,²⁶⁹ who were standing around in a close crowd, realized that she was intending to construct the first proposition of Euclid, they immediately began to break out in acclaim and applause of Euclid. Geometry herself was greatly pleased by this ovation, realizing that she too was being extolled and elevated by the recognition accorded to one of her followers; and she quickly snatched from his hands his books, which she by chance observed him carrying, and she offered them to Jove and the heavenly company as texts for further teaching and instruction. Through this performance of hers she was acknowledged to be the most learned and generous of all the bridesmaids.