A history of Greek mathematics - Wilbourhall.org

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PROCLUS. MARINUS 537
straight lines in a figure formed by taking a triangle with
sides 3, 4, 5 as ABG, then drawing
BD from the right angle B perpendicular
to AG, and lastly drawingperpendiculars
BE, BF to AB, BC.
A diagram in the text with the
lengths of the segments shown alongside
them in the usual numerical
notation shows that Paterius obtained from the data AB = 3,
BG = 4, CA = 5 the following
£Z) = |S/ lf'=2^ [=2|]
42>=«S«V = lHA [=lf]
w = /3 s *y = 2f
j i T 5 [=2|f]
^ = .^^=11^* [=i«]
BE=aSy' »? v' = 1H A A [
= Iff]
This is an example of the Egyptian method of stating fractions
preceding by some three or four centuries the exposition
of the same method in the papyrus of Akhmim.
Marinus of Neapolis, the pupil and biographer of Proclus,
wrote a commentary or rather introduction to the Data of
Euclid. 1 It is mainly taken up with a discussion of the
question ri to deSo/ievov, what is meant by given 1 There
were apparently many different definitions of the term given
by earlier and later authorities. Of those who tried to define
it
in the simplest way by means of a single differentia, three
are mentioned by name. Apollonius in his work on vevaei?
and his ' general treatise ' (presumably that on elementary
geometry) described the given as assigned or fixed (reTay-
\xkvov), Diodorus called it kno%vn (yvdopifiov); others regarded
it as rational {p-qrov) and Ptolemy is classed with these, rather
oddly, because ' he called those things given the measure of
which is given either exactly or approximately'. Others
1
See Heiberg and Menge's Euclid, vol. vi, pp. 234-56.