## On Ancient Measure, Volume 2 |

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analogy analysis Anaxagoras Ancient Medicine Archytas arguments Aristotle arithmetic assumption atomists basis bigness and smallness commensurable conception constitute construction cosmic criticism defined definition determine diagonal dialectical dialogue distinction distinguished divided line doctrine of measure earlier elementary triangles Eudoxus excess and defect explained fact finite forms of bigness fragments geometric atoms geometric mean golden section grades harmonic means human hypothetical identified incommensurable ratios indivisible lines infinite repetition intervals kind of measure knowledge mathematical ment method motions musical scale mutual subtraction natural kinds numerical ratios objects offspring of limit opposites Parmenides passage perceptible things Phaedo Philebus Philolaus philosophical Plato pleasures and pains preceding chapter Protagoras Pythagorean ratio of equality rational approximation regressive paradox relative measure represented Republic scale of nature sciences seen segments sensation shown similar Socrates Sophist soul species square Statesman structure Theaetetus theory of proportions Timaeus tion true swiftness tween two-directional unit unlimited