Content of type 'index'

English Index (Vol. II)

Adrastus 292 Alcinous 98 Alternate and alternately (of ratios) 134 Alternative proofs, interpolated (cf. III. 9 and following) 22: that in III. 10 claimed by Heron 23-4 Amaldi, Ugo, 30, 126 Ambiguous case of VI. 7, 208-9 Anaximander 111 Anaximenes 111 Angle: angles not less than two right angles not recognised as angles (cf. Heron, Proclus, Zenodorus) 47-9: hollow-angled figure (the re-entrant angle was exterior) 48: did Euclid extend “angle” to angles greater than two right angles in VI. 33? 275-6: “angle of semicircle” and “of segment” 4: hornlike angle 4, 39, 40: controversies about “angle of semicircle” and hornlike angle 39-42 (see also Hornlike) Antecedents (leading terms in proportion) 134 Antiparallels: may be used for construction of VI. 12, 215 Apollonius: Plane νεύσεις, problem from, 81, lemma by Pappus on, 64-5: Plane Loci, theorem from (arising out of Eucl. VI. 3), also found in Aristotle 198-200: 75, 190, 258 Application of areas (including exceeding and falling short) corresponding to solution of quadratic equations 187, 258-60, 263-5, 266-7 Approximations: 7/5 as approximation to $\sqrt{2}$ (Pythagoreans and Plato) 119: approximations to $\sqrt{3}$ in Archimedes and (in sexagesimal fractions) in Ptolemy 119: to $\pi$ (Archimedes) 119: to $\sqrt{4500}$ (Theon of Alexandria) 119 Archimedes: Method of, 40: Liber assumptorum, proposition from, 65: approximations to $\sqrt{3}$, square roots of large numbers, and to $\pi$ 119: extension of a proportion in commensurables to cover incommensurables 193: 136, 190 Archytas: proof that there is no numerical geometric mean between n and n + 1 295 Aristotle: indicates proof (pre-Euclidean) that angle in semicircle is right 63: on def. of same ratio (=same ἀνταναίρεσις) 120-1: on proportion as “equality of ratios” 119: on theorem in proportion not proved generally till his time 113: on proportion in three terms (συνεχής, continuous), and in four terms (διῃρημένη, discrete) 131, 293: on alternate ratios 134: on inverse ratio 134, 149: on similar rectilinear figures 188: has locus-theorem (arising out of Eucl. VI. 3) also given in Apollonius’ Plane Loci 198-200: on unit 279: on number 280: on non-applicability of arithmetical proofs to magnitudes if these are not numbers 113: on definitions of odd and even by one another 281: on prime numbers 284-5: on composite numbers as plane and solid 286, 288, 290: on representation of numbers by pebbles forming figures 288 Arithmetic, Elements of, anterior to Euclid 295 August, E. F. 23, 25, 149, 238, 256, 412 Austin, W. 172, 188, 211, 259 Axioms tacitly assumed: in Book V. 137: in Book VII. 294

Index of Greek Words and Forms (Vol. II)

ἄκρος, extreme (of numbers in a series) 328, 367: ἄκρον καὶ μέσον λόγον τετμῆσθαι, “to be cut in extreme and mean ratio” 189