15 ;;Quote: Pythagoreans saw numbers as the primary natures, the elements of all things; including justice, soul, mind, musical modes, relations, heaven

19 ;;Quote: for Plato, beings are ideas, sensible objects are defined via ideas, and sensible objects participate in the ideas that designate them

19+;;Quote: Plato thought it impossible to find a common definition for sensible things; they change too much

19 ;;Quote: mathematical entities are eternal, unchanging, and many alike; intermediate between changeable objects and unique ideas

19+;;Quote: each idea is unique

23 ;;Quote: the most elementary things form other things by combination; minute-particled and the subtlest of bodies

26 ;;Quote: Plato's forms explain visible things by inventing an equal number of other things

36 ;;Quote: the principles of eternal things are necessarily true; they explain the being of other things; e.g., fire is why things are hot

36+;;Quote: to explain something, find what provides that trait; e.g., fire, being the hottest, is the reason why other things are hot; a prototype

36 ;;Quote: there is a definite beginning and the reasons for things are not infinite

36+;;Quote: there can be no infinite regress in the production of things

36+;;Quote: where there is no first term, there is no explanation at all; no infinite regress

36+;;Quote: we know when we know how to explain adequately; adding factors infinitely should take endless time

58 ;;Quote: objects are what is sensed and not ideas; things come and go; e.g., combining two bodies and the present time

68 ;;Quote: it is impossible for anything to be and not to be; the most certain of principles

73 ;;Quote: if contradictories coexist then all things are one, mixed together, and nothing would truly belong to anything

81 ;;Quote: perception is not of itself; what moves is prior in nature to what is moved

83 ;;Quote: law of excluded middle; must either assert or deny; true or false

84 ;;Quote: definition arises from stating what we mean; i.e., the statement of which the word is a sign becomes a definition

90 ;;Quote: elements can not be analyzed further; e.g., a syllable of speech; if divided, its parts are the same as in water

95 ;;Quote: things are continuous which move together and cannot do otherwise; constitute a unit; still more when they cannot be bent; e.g., thigh vs. leg

95 ;;Quote: things are united when they do not differ in a form that is indistinguishable to sense; e.g., wine and water

96 ;;Quote: things are one when they are of the same kind or genus, despite differentiae; e.g., animals

96 ;;Quote: things are one when they share the same definition; e.g., despite size differences

96+;;Quote: any definition is divisible

96 ;;Quote: things are one when they do, undergo, have, or relate to something in common

96+;;Quote: things are primarily one when their primary being is one

96 ;;Quote: something is one if it has a form; e.g., the parts of a shoe is not a shoe if scrambled together

127 ;;Quote: there is no science of accidental being; no systematic account of the extraordinary; science concerns what is always or normally so

153 ;;Quote: definition concerns forms and their parts; must distinguish parts that belong to concrete objects but not their form

155 ;;Quote: soul is man's primary being and the body is his material; man is both body and soul; as is animals

157 ;;Quote: define by genus together with successive differentia; e.g., animal that is biped that is featherless

157 ;;Quote: classify by primary being or form, not by accidental characteristics; e.g., divide footed animals into cloven and uncloven, but not feathered or featherless

196 ;;Quote: geometric proofs discovered by construction; knowing is an act

196+;;Quote: it is obvious that an angle inscribed in a semicircle is a right angle; from three equal radii and the knowledge of triangles

218 ;;Quote: male and female is not an essential difference; the same seed may produce either depending on circumstances

222 ;;Quote: mathematical entities have no independent being; they are neither ideas nor sensible primary beings

222+;;Quote: science deals with forms, not sensible primary beings nor mathematical entities

227 ;;Quote: the science of philosophy studies the attributes and contraries of being as being; a single common reference

229 ;;Quote: to argue, every word must indicate one definite thing, a necessary connection; opposite statements are impossible

243 ;;Quote: changes, agents, and movers may be accidental, internal/partial, or essential

243 ;;Quote: any movement involves an agent, a thing moved, a start-point, and a culmination

243+;;Quote: the forms or places into which things are moved, are themselves unmoved; e.g., knowing and heating vs. knowledge and heat

255 ;;Quote: an individual is the direct source of another individual; there are no general explanatory factors; may share a common formula

256 ;;Quote: time and change have always been

256+;;Quote: time is either the same as change or is in some way bound up with it

256+;;Quote: no continuous change except locomotion, and no continuous locomotion except cyclical

258 ;;Quote: the first heaven is eternal with unceasing and cyclical motion

258+;;Quote: there is an unmoved mover that moves the first heaven; eternal and primary

261 ;;Quote: the planets are moved by 47 moving and countermoving spheres; one for each movement of a planet

264 ;;Quote: the end of every movement must be one of the divine bodies moving in the sky; no other ultimate source for movement; no infinite regress

269 ;;Quote: ideas and numbers can not produce a continuum nor explain movement

269+;;Quote: sensible objects, ideas, numbers, and contraries do not explain movement or the eternal; there must be something else

318 ;;Quote: mathematical entities are not separate from sensible things; not first principles; no coherency