AUTOLYCUS OF PITANE 
349 
Both works have been well edited by Hultsch with Latin 
translation. 1 They are of great interest for several reasons. 
First, Autolycus is the earliest Greek mathematician from 
whom original treatises have come down to us entire, the next 
being Euclid, Aristarchus and Archimedes. That he wrote 
earlier than Euclid is clear from the fact that Euclid, in his 
similar work, the Phaenomena, makes use of propositions 
appearing in Autolycus, though, as usual in such cases, giving 
no indication of their source. The form of Autolycus’s proposi 
tions is exactly the same as that with which we are familiar 
in Euclid ; we have first the enunciation of the proposition in 
general terms, then the particular enunciation with reference 
to a figure with letters marking the various points in it, then 
the demonstration, and lastly, in some cases but not in all, the 
conclusion in terms similar to those of the enunciation. This 
shows that Greek geometrical propositions had already taken 
the form which we recognize as classical, and that Euclid did 
not invent this form or introduce any material changes. 
A lost text-book on Sphaeric. 
More important still is the fact that Autolycus, as well as 
Euclid, makes use of a number of propositions relating to the 
sphere without giving any proof of them or quoting any 
authority. This indicates that there was already in existence 
in his time a text-book of the elementary geometry of the 
sphere, the propositions of which were generally known to 
mathematicians. As many of these propositions are proved 
in the Sphaerica of Theodosius, a work compiled two or three 
centuries later, we may assume that the lost text-book proceeded 
on much the same lines as that of Theodosius, with much the 
same order of propositions. Like Theodosius’s Sphaerica 
it treated of the stationary sphere, its sections (great and 
small circles) and their properties. The geometry of the 
sphere at rest is of course prior to the consideration of the 
sphere in motion, i. e. the sphere rotating about its axis, which 
is the subject of Autolycus’s works. Who was the author of 
the lost pre-Euclidean text-book it is impossible to say ; 
1 Autolyci De sphaera quae movetur liber, De ortibus et occasibus libri duo 
edidit F. Hultsch (Teubner 1885).