342 



GREEK SCIENCE. 



Analysis 

 of the 

 Almagest. 



Theorems 

 in trigono- 

 metry. 



Climates. 



Length of 

 the year, &c. 



philosophers, we should certainly not have laid before our readers this 

 extract from the introduction to the * Almagest ;' but considering it 

 as the defence of an hypothesis, which maintained its ascendency for 

 fourteen centuries amongst all nations, and which is still held sacred 

 throughout every part of Asia, it is impossible to divest it of its 

 interest and importance. 



The other part of this great work is more worthy of the talents of 

 its author, and is more deserving of our attention ; but the limits of 

 this article will not admit of our giving more than a very concise 

 abstract of its contents. The first book, beside what we have hitherto 

 mentioned, exhibits a highly-interesting specimen of the ancient trigo- 

 nometry; and the method of computing the chords of arcs, which, in 

 fact, involves our fundamental theorems of trigonometry, though 

 expressed in a manner totally different. 



Ptolemy first shows, how to find the sides of a pentagon, decagon, 

 hexagon, square, and equilateral triangle, inscribed in a circle, which 

 he exhibits in parts of the diameter, this being supposed divided into 

 120. He next demonstrates a theorem equivalent to our expression 

 sin (a b) = sin a cos b sin 6 cos a; by means of which he finds 

 the chord of the difference of any two arcs, whose chords are known. 

 He then finds the chord of any half arc, that of the whole arc being 

 given, and then demonstrates what is equivalent to our formula for 

 the sine of two arcs ; that is, sin (a-f-6) = sin a cos b -f- sin b cos a ; 

 and by means of this he computes the chord to every half degree of 

 the semicircle. These theorems it may be said belong rather to the 

 history of trigonometry than to that of astronomy ; but we trust that 

 the obvious dependence of the latter science upon the former, will 

 be found to justify us in introducing them to the reader in this place. 



We are next presented with a table of climates nearly equivalent to 

 our nonagesimal tables, and it is not a little singular, that amongst 

 them, we find none appertaining to the latitude of Alexandria; 

 because, without such an auxiliary, Ptolemy must have contented 

 himself with interpolations, which were not only difficult to make, 

 but attended at the same time with great inaccuracy ; a circumstance 

 from which it has been concluded, that Ptolemy himself made few 

 observations, or that he was not very particular concerning the 

 accuracy of his calculations. The examination of this question would 

 carry us too far out of our track to admit of our entering upon it in 

 this place ; but the reader may see it developed in all requisite detail, 

 in the learned ' History of Astronomy,' lately published by Delambre. 



Having passed over the above preliminary details, the author treats 

 of the length of the year, the motion of the sun, the mean and 

 apparent anomaly, &c. &c. The length of the year, according to the 

 sexagesimal notation, he makes 365d. 14' 48", which answers to 

 365d. 5h. 55' 12" ; the diurnal motion of the sun is stated to be 

 59' 8" 1"' 13 iv 12 V 31 vi , and the horary motion 2' 27" 50'" 

 43 iv 3 V l vi . To this is also added two tables, one of the mean 



