The philosophical and mathematical commentaries of Proclus on the first book of
- Language:
- English
- Status:
- Complete work
- Authorship:
- Written by the author
- Condition of the text:
- No scanning noise detected (automatic measure over the whole text, not checked by hand)
- Extent:
- ~130,000 words · 599 passages
Cite this work
- APAProclus. (n.d.). The philosophical and mathematical commentaries of Proclus on the first book of. Digital reproduction: SigPhi. https://sigphiai.com/en/works/proclus/the-philosophical-and-mathematical-commentaries-of-proclus-on-the-first-book-of
- MLAProclus. The philosophical and mathematical commentaries of Proclus on the first book of. Digital reproduction, SigPhi, https://sigphiai.com/en/works/proclus/the-philosophical-and-mathematical-commentaries-of-proclus-on-the-first-book-of.
- ChicagoProclus. The philosophical and mathematical commentaries of Proclus on the first book of. Digital reproduction, SigPhi. https://sigphiai.com/en/works/proclus/the-philosophical-and-mathematical-commentaries-of-proclus-on-the-first-book-of.
Reference to the edition that SigPhi reproduces: SigPhi is its digital reproduction, not its publisher. The edition's year is not in the metadata (hence "n.d."), and the translator appears only when recorded.
What it is about
Proclus's commentary on the first book of Euclid's 'Elements': at once a philosophy of mathematics and the main source we have for the history of Greek geometry.
Context and history
Proclus wrote it in the fifth century, eight hundred years after Euclid, and its value is twofold. As philosophy, it defends a position still argued over: mathematical objects are neither things in the world nor conventions, but exist in the imagination as the projection of reasons the soul already holds. As a document, it contains the 'catalogue of geometers', a summary of the history of geometry before Euclid derived from a lost work of Eudemus, and this is nearly all we know about the beginnings of Greek mathematics. Without these pages, Thales and Pythagoras as mathematicians would be even dimmer than they are. The translation is Thomas Taylor's, of 1788.
Editorial context, not a citable source: unlike the passages of the work itself, these statements cannot be checked against the corpus.
conceptions. “For, in the first place (says Syrianus[7]), there are no ideas of things evil and base, because these subsist in nature rather by a privation and absence of ideas. And, on this account, they are said to exist contrary to nature. Nor, secondly, of negations, for these are destructive of the bound and limitation which is attributed to every thing from the unifying and comprehending nature of ideas; and hence, separation is rather the result of material infinity than of that which is formal or ideal. Nor again, are there any ideas of things which at different times receive a variety of conditions. For these participate of transmutation from a moveable cause, but not from the immoveable and stable illustration of ideas. Nor again of parts, such as the hand, head, fingers, and the like. For the causes of things existing entire, produce whole species and forms; not divided about the parts of these, like the reasons of nature. But neither did these wise men place in intellect the determinate causes of accidents in bodies, such as sweetness and whiteness. For they considered that natural reasons were sufficient for the production of accidents. Nor again, of composites, as of a wise man. For since ideas are simple, they preside over the simple essence of every thing. But the composition and division of things is the business of our intellect; ideas, at the same time, and that intellection which is co-ordinate to ideas, being exempt from all these, on account of superlative simplicity. Neither, therefore, must we establish ideas of things generated from dissimilars, such as mules; nor of fruit produced by engrafting from different trees. For all these have a posterior and adventitious generation, and are not the work of nature alone, nor of nature proceeding according to her own reasons, but, as it were, compelled to labour contrary to her own determinations.…