430
EUCLID
therefore
(arc ABC) = (arc DCE), and (segmt. ABC) = (segmt. DCE);
therefore (sector A DBG), or — (circle ABC)
= (segmt. DCE) — (segmt. BFC).
That is BC, DE cut off an area equal to ^ (circle ABC).
Lost geometrical works.
(a) The Pseudaria.
The other purely geometrical works of Euclid are lost so far
as is known at present. One of these again belongs to the
domain of elementary geometry. This is the Pseudaria, or
‘Book of Fallacies’, as it is called by Proclus, which is clearly
the same work as the ‘ Pseudographemata ’ of Euclid men
tioned by a commentator on Aristotle in terms which agree
with Proclus’s description. 1 Proclus says of Euclid that,
‘ Inasmuch as many things, while appearing to rest on truth
and to follow from scientific principles, really tend to lead one
astray from the principles and deceive the more superficial
minds, he has handed down methods for the discriminative
understanding of these things as well, by the use of which
methods we shall be able to give beginners in this study
practice in the discovery of paralogisms, and to avoid being
ourselves misled. The treatise by which he puts this machinery
in our hands he entitled (the book) of Pseudaria, enumerating
in order their various kinds, exercising our intelligence in each
case by theorems of all sorts, setting the true side by side
with the false, and combining the refutation of error with
practical illustration. This book then is by way of cathartic
and exercise, while the Elements contain the irrefragable and
complete guide to the actual scientific investigation of the
subjects of geometry.’ 2
The connexion of the book with the Elements and the refer
ence to its usefulness for beginners show that it did not go
beyond the limits of elementary geometry.
1 Michael Ephesius, Comm, on Arist. Soph. El., fob 25 v , p. 76. 28 Wallies.
2 Proclus on Eucl. I, p. 70. 1-18. Cf. a scholium to Plato’s Theaetetus
191 B, which says that the fallacies did not arise through any importation
of sense-perception into the domain of non-sensibles.
