The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elementsProclus
Philosophy
The philosophical and mathematical commentaries of Proclus on the first book of Euclid's elements (Vol. 1 of 2) : $b To which are added, A history of the restoration of Platonic theology, by the latter Platonists: And a translation from the Greek of Proclus's Theological elements
Proclus
Euclid. Elements; Platonists
[153] Mr. Simson, in his note on this definition, supposes it to
be the addition of some less skilful editor; on which account, and
because it is quite useless (in his opinion) he distinguishes it from
the rest by inverted double commas. But it is surely strange that the
definition of angle in general should be accounted useless, and the
work of an unskilful geometrician. Such an assertion may, indeed, be
very suitable to a professor of experimental philosophy, who considers
the useful as inseparable from practice; but is by no means becoming
a restorer of the liberal geometry of the ancients. Besides, Mr.
Simson seems continually to forget that Euclid was of the Platonic
sect; and consequently was a philosopher as well as a mathematician.
I only add, that the commentary on the present definition is, in my
opinion, remarkably subtle and accurate, and well deserves the profound
attention of the greatest geometricians.
[154] For a philosophical discussion of the nature of quality and
quantity, consult the Commentaries of Ammonius, and Simplicius on
Aristotle’s Categories, Plotinus on the genera of beings, and Mr.
Harris’s Philosophical Arrangements.
[155] That is, the ellipsis.
[156] That is, they are either right, acute, or obtuse.
[157] This oracle is not mentioned by any of the collectors of the
Zoroastrian oracles.
[158] This, indeed, must always be the case with those geometricians,
who are not at the same time, philosophers; a conjunction no less
valuable than rare. Hence, from their ignorance of principles and
intellectual concerns, when any contemplative enquiry is proposed,
they immediately ask, in what its utility consists; considering every
thing as superfluous, which does not contribute to the solution of some
practical problem.
[159] Concerning the soul’s descent into body, see lib. ix., Ennead
iv. of Plotinus; and for the method by which she may again return to
her pristine felicity, study the first book of Porphyry’s Treatise on
Abstinence.
[160] This Definition too, is marked by Mr. Simson with inverted
commas, as a symbol of its being interpolated. But for what reason
I know not, unless because it is useless, that is, because it is
_philosophical_!
[161] That is, the various species of forms, with which the four
elements are replete.
[162] That is, the circle.
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