ASTRONOMY. 335 



10. In the oblique sphere, every circle which passes through the 

 poles, will be perpendicular to the horizon twice in the course of one 

 complete revolution. 



We omit some other propositions of this author, which are of less ^ e .^ o r n 

 importance than the above ; and even those which we have given, are 4 

 such as one would imagine could not have escaped the observation of 

 any one who would think of employing an artificial sphere to represent 

 the celestial motions ; yet from the tenor of the work in question, it 

 would seem, that if they were known, they were never before, at least, 

 embodied in the form of a regular treatise. 



Here, then, we may begin to date the first scientific form of astro- 

 nomy ; because in this work, however low and elementary, we have 

 an application of geometry to illustrate the motions of the heavenly 

 bodies ; but we shall still find two other centuries pass away, before 

 the same principles were applied to actual computation. 



Contemporary with Autolycus was Euclid ; whose elements of geo- Eucli<L 300 

 metry, after so many ages, still maintain their pre-eminence, and con- 

 tain all the propositions that are necessary for establishing every useful 

 theorem in trigonometry ; yet it is perfectly evident that no ideas were 

 yet conceived of the latter science. Neither Euclid nor Archimedes, 

 great as were their skill and talents in geometry, had any idea of the 

 method of estimating the measure of any angle by the arc, which the 

 two lines forming it intercepted ; nor does it appear that they knew 

 of any instrument whatever for taking angles ; a very convincing proof 

 of which appears in the process adopted by the latter justly-celebrated 

 philosopher, in order to determine the apparent diameter of the sun. 



Passing over the poet Aratus, who is supposed to have embodied Aristarchus. 

 in his poem all the astronomical knowledge of the time in which he 

 wrote, viz., 270 B. c., but who had not himself made any observa- 

 tions, we come to Aristarchus, who has left us a work, entitled * Of 

 Magnitudes and Distances;' in which he teaches, that the moon re- 

 ceives her light from the sun, and that the earth is only a point in 

 comparison with the sphere of the moon. He likewise added, that 

 when the moon is dichotomized, we are in the plane of the circle which 

 separates the enlightened part from the unenlightened, Which is the 

 most curious and original remark of this author ; in this state of the 

 moon, he also observes, that the angle subtended by the sun and moon, 

 is one-thirtieth less than a right angle ; which, in other words, is say- 

 ing, that the angle is 87, whereas we now know that this angle ex- 

 ceeds 89 50'. In another proposition he asserts, that the breadth of 

 the shadow of the earth is equal to two semi-diameters of the moon, 

 whereas these are to each other as 83 to 64. In his sixth proposition, 

 he states the apparent diameter of the moon to be one-fifteenth part 

 of a sign, or 2 ; whereas we know that it is only about half a degree. 

 Again, the distance of the earth from the moon being assumed as unity, 

 the distance of the moon from the sun was said to be 17*107, and the 

 distance of the earth from the sun 19*081. Such was the astronomical 



