THE ‘THEOREM OF PYTHAGORAS’ 
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the solution of the problem, ‘ given two figures, to apply 
a third which shall be equal to the one and similar to 
the other’, and he adds that this problem is unquestionably 
finer than the theorem about the square on the hypotenuse. 
But Athenaeus and Porphyry 1 (a.D. 233-304) connect the 
sacrifice with the latter proposition ; so does Diogenes Laertius 
in one place. We come lastly to Proclus, who is very cautious, 
mentioning the story but declining to commit himself to 
the view that it was Pythagoras or even any single person 
who made the discovery: 
‘ If we listen to those who wish to recount ancient history, 
we may find some of them referring this theorem to Pytha 
goras, and saying that he sacrificed an ox in honour of his 
discovery. But for my part, while I admire those who first 
observed the truth of this theorem, I marvel more at the 
writer of the Elements, not only because he made it fast by a 
most lucid demonstration, but because he compelled assent to 
the still more general theorem by the irrefutable arguments of 
science in the sixth book.’ 
It is possible that all these authorities may have built upon 
the verses of Apollodorus ; but it is remarkable that, although 
in the verses themselves the particular theorem is not speci 
fied, there is practical unanimity in attributing to Pythagoras 
the theorem of Eucl. I. 47. Even in Plutarch’s observations 
expressing doubt about the particular occasion of the sacrifice 
there is nothing to suggest that he had any hesitation in 
accepting as discoveries of Pythagoras both the theorem of the 
square on the hypotenuse and the problem of the application 
of an area. Like Hankel, 2 therefore, I would not go so far as 
to deny to Pythagoras the credit of the discovery of our pro 
position ; nay, I like to believe that tradition is right, and that 
it was really his. 
True, the discovery is also claimed for India. 3 The work 
relied on is the Apastamba-Sulba-Sutra, the date of which is 
put at least as early as the fifth or fourth century b.c., while 
it is remarked that the matter of it must have been much 
1 Porphyry, Vit. Pyth. 36. 
2 Hankel, Zur Geschichte der Math, in Alterthum und Mittelalter, p. 97. 
3 Bürk in the Zeitschrift der morgenland. Gesellschaft, Iv, 1901, 
pp. 543-91 ; Ivi, 1902, pp. 327-91. 
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