A Source Book in Greek Science

Author: Claudius Ptolemy

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The Elements of Geography

Ptolemy, Geography I. 1–5 (Müller)3

1. Wherein geography differs from chorography

Geography is the representation, by a map, of the portion of the earth known to us, together with its general features. Geography differs from chorography in that chorography concerns itself exclusively with particular regions and describes each separately, representing practically everything of the lands in question, even the smallest details, such as harbors, villages, districts, streams branching from the principal rivers, and the like. It is the task of geography, on the other hand, to present the known world as one and continuous, to describe its nature and position, and to include only those things that would be contained in more comprehensive and general descriptions, such as gulfs, large cities and nations, the more important rivers, in short the more significant instances of each type.

The purpose of chorography is the description of the individual parts, as if one were to draw merely an ear or an eye; but the purpose of geography is to gain a view of the whole, as, for example, when one draws the whole head.

Now in the case of the drawings just referred to, the principal parts are of necessity fitted in first, and must be properly proportioned, when seen from a suitable distance, to the spaces on the surface used for the drawing (whether the drawing be of an entire object or of only a part), in order that the representation may be perceived as a whole. It is consequently both reasonable and proper that chorography should represent the smaller particular details and geography the regions themselves with the general features that belong to them. For the principal features of the inhabited earth and those most readily fitted in on the proper scale are the various regions themselves in their proper location; while the principal features of these regions are the peculiar details of the land in question.

Again, chorography deals, for the most part, with the nature rather than with the size of the lands. It has regard everywhere for securing a likeness but not, to the same extent, for determining relative positions. Geography, on the other hand, is concerned with quantitative rather than with qualitative matters, since it has regard in every case for the correct proportion of distances, but only in the case of the more general features does it concern itself with securing a likeness, and then only with respect to configuration.

Therefore chorography has need of topography, and no one can be a chorographer unless he is also skilled in drawing. But geography has no such absolute need of topography, for by using mere lines and annotations it shows positions and general outlines. For this reason, while chorography does not require the mathematical method, in geography this method plays the chief part.

For geography must first consider the form of the whole earth as well as its size and its position with reference to the heavens, so that it may be able to tell the size and nature of the known portion of the earth and under what parallel circles of the celestial sphere each place lies. From this it will be possible to learn the length of nights and days, the fixed stars that are overhead and those that at all times are above or below the horizon, as well as all other information that we include in an account of habitable regions.

These are studies that form a part of the most sublime and beautiful theoretic science, for it is with the aid of mathematics that they reveal to man’s understanding the heaven itself in its true nature (for we can observe it as it rotates about us); while they represent the earth through a model, since the real earth, which is so great and does not surround us, cannot be traversed in its entirety or in its individual parts by the same men.

2. The foundations of geography

The above account should suffice as a general outline of the purpose of the geographer and wherein he differs from the chorographer.

Since we have now undertaken to map our inhabited world in such a way as to approximate the proportions of the real world as closely as possible, we think that we should explain beforehand that in this procedure the descriptions given by travelers are of the highest importance. For we gain our greatest knowledge from the reports of those travelers through the various regions who have theoretic understanding of geography. Again, their observations and reports may be based either on geometrical or astronomical measurement. Now geometry indicates the relative positions of places by simple measurement of distances, while astronomy uses observational data obtained with astrolabes and sundials. The astronomical method is self sufficient and more accurate, but the geometrical method is rougher and requires the astronomical to supplement it.

Now since in either case it is necessary to determine in what direction the line joining two given places lies (for it is necessary to know not merely the distance between the places but also the direction, whether it be, e.g., to the north or the east or some line intermediate between them), it is impossible to perform this investigation accurately without observation by means of the aforesaid instruments. For with their help the position of the meridian may be obtained at any time and place, and, as a consequence, the direction of distances traversed.

But even if this is found, the measurement in stades does not give us an accurate knowledge of the true distance, since our course rarely coincides with straight lines but, on the contrary, shows many deviations both on land and on sea. Now in the case of journeys on land it is necessary, in order to find the length in a straight line, to subtract from the whole number of stades traversed the excess due to the nature and number of the deviations, as estimated. In the case of sea voyages allowance must be made for variations due to the winds, which do not in general preserve a constant intensity. But even if the distance between two places is accurately measured, this does not give us the ratio of that distance to the whole circumference of the earth or its position with respect to the equator and the poles.

But measurement based on celestial observation gives each of these things accurately. It shows how great are the arcs mutually intercepted by the parallel circles and the meridians (i.e., the arcs of the meridians falling between the parallel circles and the equator, and the arcs of the equator and the parallels falling between the meridians); it also shows how great an arc the two places in question intercept on a great circle of the earth drawn through them. And this method does not require us to compute the number of stades in order to obtain the ratio of the various parts of the earth to one another and for the general procedure of drawing our map. For it is sufficient to take the circumference of the earth, divided into as many parts as desired, and to show how many such parts of a great circle of the earth there are in each of the several distances examined.1

But naturally this method does not suffice for the division of the whole circumference or parts of it into actual distances familiar to us by our own measurements. And for this reason alone it has become necessary to compare some straight distance on the earth with the similar arc of a great circle on the celestial sphere, and, obtaining by observation the proportion of this arc to the whole circle, and, by measurement based on some given part, the number of stades in the terrestrial distance under this arc, to find the number of stades in the whole circumference.2

For we assume on the basis of mathematics1 that the surface of the earth and sea taken together is substantially spherical, having as center the center of the celestial sphere, so that every plane passed through the center cuts the aforesaid surfaces2 in great circles, and the angles subtended at the center intercept similar arcs on these circles,3 Now, though the number of stades in terrestrial distances along a straight line can be obtained by measurement, the ratio of this distance to the whole circumference of the earth can not be obtained by measurement because of the impossibility of a comparison.4 This ratio can, however, be obtained from the fact that the arc subtended on the celestial sphere is similar.5 For it is possible to obtain the ratio of this arc to the whole celestial circumference. And the ratio of a similar arc on the earth to the great circle of the earth is the same.

3. A method of finding the number of stades in the circumference of the earth, given any distance in stades along a straight line, not necessarily on the same meridian; and conversely

Now our predecessors sought not only a rectilinear terrestrial distance (so that it would constitute an arc of a great circle)6 but one lying in the plane of a single meridian. Observing by sun dials the points overhead7 at the two places between which the distances lay, they immediately obtained an arc on the meridian joining these places equal to the arc over which a journey would be made, because the places lay, as we said, on the same plane.8 Moreover, straight lines drawn through the places in question to the points directly overhead met each other when produced, and the common center of the circles was the point of intersection of these lines. Now they took the ratio of the arc between the points overhead to the whole circle passing through the celestial poles as equal to the ratio of the terrestrial distance in question to the circumference of the whole earth.

But even if the great circle on the earth’s surface that includes the measured distance does not pass through the poles, but is any great circle, we have demonstrated that our problem may still be solved by similar observations of the elevation of the pole at the terminal points and the position which the terrestrial distance has with reference to each meridian. This we have done by constructing an instrument1 for viewing the heavenly bodies. With this instrument we easily obtain many very useful facts, but in particular (1) on any day or night the elevation of the north pole at the point from which the observation is made;2 (2) at every hour not only the position of the meridian but also the position with reference to it of any land route, i.e., the angle made by the great circle drawn through the route and the meridian passing through the zenith.3

Using these angles we may alike determine both the required arc, with the sole help of the instrument, and also the arc cut off by two meridians on parallels other than the equator. And so, with this method, by measuring only one straight distance on the earth we can find the number of stades in the whole circumference, and furthermore, knowing this we can then find without actual measurement the number of stades in any other distance. And we can do this even when the distances are not entirely straight4 and do not lie on the same meridian or parallel of latitude. It is necessary, however, that the precise direction of the distance be carefully observed, as well as the latitude of the termini, for it is from the ratio that the arc representing the distance in question bears to the great circle that the number of stades in such distance can be easily computed, given the circumference of the whole earth.

4. Actual observations of phenomena are to be preferred to reports of travelers

This, then, being the case, if those who have traveled over the several countries had made use of this type of observation, it would have been possible to make a completely accurate map of the inhabited earth. But Hipparchus alone gave us the elevation of the north pole [i.e., the latitude] for a few cities of the multitude that must be included in a description of the earth, and indicated places that lie on the same parallels, while some of his successors recorded some of the cities that lie opposite each other (not those equally distant from the equator, but merely those lying on the same meridian), on the basis of sailings made between these places with the aid of north or south winds. Again, most distances, especially those to the east or west, were given quite roughly, not by reason of the carelessness of those who made these investigations but probably because of the fact that the more strictly mathematical method of observation had not yet been adopted, and it had not been considered important to record sufficiently numerous observations of lunar eclipses on the same occasion in different places. I refer to an eclipse like that observed at Arbela at the fifth hour and at Carthage at the second, from which the distance of the two places from each other eastward or westward could have been determined in equinoctial hours.1 For these reasons it would be proper for one who is to make a map of the earth in accordance with these principles to use the data obtained by more accurate observations as the foundation for the map, and to fit in with these data those obtained from other sources, until the positions indicated in the latter data both in relation to one another and in relation to the fundamental data are in accord, in so far as is possible, with the more accurate traditions.

5. Attention must be paid to more recent accounts because of changes in the earth with passage of time

The construction of the maps, therefore, would be best accomplished on the basis of the principles described. But in the case of regions which are not completely known either because of their great size or because they do not always present the same aspect, later reports give us a more accurate account each time, and this is true in connection with geography, too. For the various historical accounts themselves agree that many divisions of the inhabited portion of our earth have not yet come to be known because of the difficulties occasioned by their size. Again, other divisions have not been accurately described because of carelessness on the part of those who received reports, and some parts are themselves different from what they were formerly because of destruction or changes that have taken place in them. For these reasons it is necessary that here, too, we pay heed in general to the last reports that come to us, distinguishing that which is worthy of belief and that which is not, both in our use of the new data and in our judgment of what had previously been reported.

1 I.e., distances may be represented merely in degrees of arc independently of the number of stades to a degree.

2 A given terrestrial distance, lying theoretically on the arc of a great circle, is measured in stades; the ratio of this arc to the whole circumference is then determined by astronomical observation, whence the measurement of the whole circumference in stades may be found. The measurements by Eratosthenes and Posidonius are examples of this method (see pp. 149–153, above).

1 See the proofs of Aristotle and Archimedes, p. 236.

2 I.e., the surfaces of the terrestrial and celestial spheres.

3 Since any central angle intercepts similar arcs on concentric circles, i.e., arcs equal in circular, but not in linear, measure.

4 I.e., a comparison between the terrestrial distance and the terrestrial circumference.

5 I.e., equal in degrees to the arc represented by the distance in question on the terrestrial sphere.

6 The "rectilinear" or shortest distance between two points on the surface of a sphere is the arc of the great circle joining the points.

7 I.e., the angular distance from the sun (e.g., at noon of the equinox) to the zenith.

8 I.e., on the same plane passing through the earth’s diameter, or, in other words, on the same meridian. The arc thus measures the difference in latitude between the two places.

1 The reference is to the ring astrolabe described in the Almagest (see p. 134, above).

2 This would be the latitude of the observer.

3 This angle together with the readily obtained latitude of the two places would, theoretically, determine the distance, in circular measure, of the route in question. The practical difficulties of measuring longitude in antiquity would be reflected in the application of the method.

4 Perhaps the reference is to places separated by mountains. In any case, however, Ptolemy would theoretically be able, either by trigonometry or by using globe and compass, to find the distance, along an arc of a great circle, between any two places whose latitude and longitude have been determined. But the chief difficulty lay in the determination of the longitude of a place before instantaneous communication became possible. The best available method was that of noting the time when a lunar eclipse was seen in two different cities. Since the eclipse is seen at about the same time in both places, the difference in the local time (i.e., the number of hours after sunrise or sunset) will indicate the difference in longitude, at the rate of 15° for each hour. Because of the unreliability of timekeeping instruments in antiquity the method described furnished only a rough approximation, and reports of distances as given by travelers came to be the chief basis of determining longitude. There are also references to the use of royal "pacers" in Ptolemaic Egypt for the purpose of estimating distances. The use of the hodometer (p. 342) in practice is doubtful. Of course, for short distances surveying was done with such instruments as the dioptra and the groma.

The method of determining the distance between Rome and Alexandria is taken up by Hero of Alexandria (Dioptra, 35); see O. Neugebauer, op. cit. (p. 136, n. 2, above).

1 As a matter of fact, however, the case illustrates the difficulty of accurately determining longitude by lunar eclipses or any other means in the absence of dependable clocks. The three hours’ difference corresponds to a difference in longitude of 45° more than 11° greater than the actual difference between Carthage and Arbela. The eclipse, which is referred to by many ancient authors, is probably that of Sept. 20, 331 B.C. Cf. Pliny, Natural History II. 180: "At Arbela, upon the victory of Alexander the Great, the moon is said to have been eclipsed at the second hour of the night, whereas the eclipse took place in Sicily as the moon was rising." The reference to the hour of occurrence is fairly accurate in Pliny’s account but not in Ptolemy’s, according to modern computations. (See H. v.

Des Klaudios Ptolemaios Einführung in die darstellende Erdkunde, pt. I [Vienna, 1938], p. 21, n. 3.) But the eclipse seems to have preceded the battle by 11 days.


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Chicago: Claudius Ptolemy, "The Elements of Geography," A Source Book in Greek Science, ed. Müller in A Source Book in Greek Science, ed. Morris R. Cohen and I. E. Drabkin (Cambridge: Harvard University Press, 1948), 162–169. Original Sources, accessed February 20, 2020, http://originalsources.com/Document.aspx?DocID=P7CJKSWJTHPVH19.

MLA: Ptolemy, Claudius. "The Elements of Geography." A Source Book in Greek Science, edited by Müller, Vol. I, in A Source Book in Greek Science, edited by Morris R. Cohen and I. E. Drabkin, Cambridge, Harvard University Press, 1948, pp. 162–169. Original Sources. 20 Feb. 2020. originalsources.com/Document.aspx?DocID=P7CJKSWJTHPVH19.

Harvard: Ptolemy, C, 'The Elements of Geography' in A Source Book in Greek Science, ed. . cited in 1948, A Source Book in Greek Science, ed. , Harvard University Press, Cambridge, pp.162–169. Original Sources, retrieved 20 February 2020, from http://originalsources.com/Document.aspx?DocID=P7CJKSWJTHPVH19.