16 
Remarks on a Passage in the 
era ; we may therefore roughly allow 6' for the diminution of 
the angle in the interval from the time of Eratosthenes, and 
we shall then have 23° 45' instead of a quantity, which is not 
widely different from the obliquity, as it was about 200 years 
ago. De la Hire rested much upon this passage, when he 
wished to shew that the angle was not liable to variation. u 11 
y a grande appai'anGe,” he says *, “ que les astronomes d’Alex- 
andrie, qui vinrent apres Ptolemee, s’appercurent bien que ses 
observations n’etoient pas fort justes, puisque Pappus, qui etoit 
aussi d’ Alexandria, et qui vivoit 270 ans apres Ptolemee, ayant 
ramasse tout ce qu'il y avoit de curieux dans les Mathemati- 
ques, dit, dans son 6 me livre, ou il rapporte 61 propositions sur 
la sphere, que Fobli quite de fecliptique etoit de 23° 80', ce qui 
etoit sans doute fort connu pour lors.” In answer to this, the 
Chevalier de Louville, who supported the opposite side of the 
question, acknowledged that the passage was against him, but 
he argued that it was a solitary authority : u Et *f* d^ailleurs il 
soutient que Pappus, dans fendroit qu’on cite, if a point pre- 
tendu donner une determination exacte, mais seulement tirer 
des racines quarrees, qui lui ont produit des nombres ap- 
prochees.” The latter part of this statement is not very clear : 
we shall find also that Pappus takes the squares instead of the 
square roots of his original numbers, and so far there is a mis- 
take ; but the former part contains the precise conclusion at 
which we must at last arrive. 
Various hypotheses have been devised to reconcile this pas- 
sage of Pappus with the authorities of Eratosthenes, Ptolemy, 
and of modem observations ; but there would be no good ob- 
tained from a minute discussion of them. The same feeling, 
however, the same wish not to lose this additional authority, 
seems to influence even Lalande and Delambre ; and their spe- 
culations call for more particular attention. 
In the last edition of his astronomy, § 2741, Lalande ad- 
mits, that the object which Pappus had in view was not to 
give an astronomical determination of the obliquity of the eclip- 
tic ; but still he evidently thinks it possible that some mistake 
may have occurred in the numbers. He says that we only 
* Mem. de V Acad. Roijale de Sciences , 1716. 
f Ibid. 
