These are the same quotation from the lost work: Iamblichus, Commentary
on Aristotle's Categories:
Simplicius, Commentary on Aristotle's Categories,
192.12-25
Simplicius, Commentary on Aristotle's Physics,
60.6-18
Curve | Mathematician | Purpose Mentioned | location |
cochloid or conchoid (described by Pappus, Collectio iv §§26-29) | Nicomedes (PI) | angle trisection (I) | 1, 2 |
sibling of the cochlioid | Apollonius, Nicomedes (I) | circle squaring (I) | 3, 4 |
conics | Apollonius (P) | 2 | |
line from double motion | Carpus (I) | circle squaring (I) | 3, 4 |
quadratrices (all sources are available) | Hippias (P), Nicomedes (PI) | cutting an angle in a given ratio (P), circle squaring (I) | 1, 2, 3, 4 |
speirics (discussed by Hero, Metrica ii 13, ps.-Hero, Definitions 74-75, and Proclus) | Perseus (P) | none | 2 |
Archimedean spiral (besides Archimedes, On Spirals, see Pappus, Collectio iv §§21-25) | others (P) | cutting an angle in a given ratio (P) | 1 |
spiral-like (= Archimedean spiral?), the line of 'Lycomedes' certainly is certainly a mistake | Archimedes (I) | circle squaring (I) | 3, 4 |
other curves not named | circle squaring (I) | 3, 4 | |
the "demonstrations of Sextus the Pythagorean" | Sextus the Pythagorean | circle squaring (I) | 3, 4 |