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
[125] The present Comment, and indeed most of the following, eminently
evinces the truth of Kepler’s observation, in his excellent work,
_De Harmonia Mundi_, p. 118. For, speaking of our author’s
composition in the present work, which he every where admires and
defends, he remarks as follows, “oratio fluit ipsi torrentis instar,
ripas inundans, et cæca dubitationum vada gurgitesque occultans, dum
mens plena majestatis tantarum rerum, luctatur in angustiis linguæ, et
conclusio nunquam sibi ipsi verborum copiâ satisfaciens, propositionum
simplicitatem excedit.” But Kepler was skilled in the Platonic
philosophy, and appears to have been no less acquainted with the great
depth of our author’s mind than with the magnificence and sublimity of
his language. Perhaps Kepler is the only instance among the moderns,
of the philosophical and mathematical genius being united in the same
person.
[126] That is, the reason of a triangular figure (for instance) in the
phantasy, or triangle itself, is superior to the triangular nature
participated in that figure.
[127] In the tenth book of his Republic.
[128] See the Hymn to the Mother of the Gods, in my translation of the
Orphic Initiations.
[129] The philosopher here seems to contradict what he asserts in the
end of his comment on the 13th Definition: for there he asserts, that
the circle is a certain plane space. Perhaps he may be reconciled, by
considering, that as the circle subsists most according to bound, when
we speculate its essence in this respect we may define it according
to the circumference, which is the cause of its bound. But when we
consider it as participating of infinity also, though not in so eminent
a degree, and view it from its emanations from the centre as well as in
its regressions, we may define it a plane space.
[130] That is, the essential one of the soul is the mother of number;
but that which subsists in opinion is nothing more than the receptacle
of the former; just as matter is the seat of all forms. For a farther
account of the subsistence of numbers, see the first section of the
preceding Dissertation.
[131] That is, number composed from units.
[132] This sentence within the brackets, is wholly omitted in the
printed Greek.
[133] In i. De Cælo.
[134] This sentence within the brackets, which is very imperfect in the
Greek, I have supplied from the excellent translation of Barocius. In
the Greek there is nothing more than λὲγω δὲ ἑνὸν τῂν γραμμὴν δυαδός
πρὸς τὸ στερεόν.
[135] In the Greek, γὰρ ἡ μονὰς ἐκεῖ πρῶτον, ὅπου πατρικὴ μονάς ἐστι
φησὶ τὸ λόγιον. The latter part only of this oracle, is to be found
in all the printed editions of the Zoroastrian oracles; though it is
wonderful how this omission could escape the notice of so may able
critics, and learned men. It seems probable, from hence, that it is
only to be found perfect in the present work.
[136] The word τανάη, is omitted in the Greek.
Public-domain text, read in full here on John Shaqi.
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