Therefore, if DK is bisected at L, L will fall between G and K, and the square on LB = LD + KB . BD. A.T-BE..D..GL—K Z-H-N▬▬▬▬M Therefore ZM2 – ZH3 = EL. LG; but DK is bisected in L, so that Therefore but also Therefore AB ==EL, but TB also = 1G Hence or Thus 16AB. BT = MZ ̊ – ZH2 = MH2 + 2ZH . HM. Therefore HM is even. Let it be bisected in N....... [Here the fragment ends.] Ab-kismet, 41 n. INDEX. [The references are to pages.] Abu'lfaraj, 2, 3, 12, 13, 41 Abu Ja'far Mohammed ibn Alhusain, Addition, how expressed by Diophantos, Algebraic notation, three stages of, 77 aljabr, 40, 92, 149-150, 158 Al-Shahrastāni, 41 Alsirāj, 24 n., 159 ἀναφορικός of Hypsikles, 5 ἀορίστως, ἐν ἀορίστῳ, 140 Arabian scale of powers compared with Arabic translations, &c., 23, 24, 25, 39-42, 148-159 Archimedes, 7, 142, 143, 144, 146, 147 Arithmetic and Geometry, 31, 141— 'Apieμntikά of Diophantos, 33 and pas- ἀριθμητική and λογιστική, 18, 136, 145 ápuós, o; Diophantos' technical use Ars rei et census, 21 n. Bacchios ὁ γέρων, 14, 15, 16 Billy, Jacobus de, 3, 54 Bombelli, 13, 14, 15, 23, 35, 36, 42- Bossut, 32, 38, 90 n., 138-139 n. Brassinne, 221 n. Lato, 70 λeîis, and the symbol for it, 66 n., 71— 73, 137, 163 λεῖψις ἐπὶ λεῖψιν πολλαπλασιασθεῖσα Lessing, 142, 143, 144, 146 n. Limits, method of, 86, 87, 115-117; approximation to, 117-120 Lousada, Miss Abigail, 56 "Majuskelcursive" writing, 64, 72 n. Manuscripts of Diophantos, 19, 61 minus, Diophantos' sign for, 66 n., 71— Minus multiplied by minus gives plus, "Minuskelcursive " writing, 64 μovádes, 69; the symbol for, 69 Montucla, 3, 11, 53, 71, 136 mufassirin, 40 n. mukābala, 92, 149–150, 158 Multiplication, modern signs for, 78 n. nâqis, 151 n. Nesselmann, 5, 10, 20, 21, 22, 23, 27, 169 n., 135, 151 Notation, algebraic: three stages, 77— Numbers which are the sum of two squares, 127-130 Numbers which are the sum of three squares, 130-131 Numbers as the sum of four squares, ὀργανῶσαι, 136 137 Oughtred, 78 n. Pappos, 11, 12, 17, 65 n., 139 120 Peletarius, James, 2, 43 Pell, John, 56 Perron, Cardinal, 20 Plato, 18, 141–142, 145 plus, Diophantos' expression of, 71, Pococke, 2, 12, 41 n. Polygonal Numbers, ¡31-35 and pas- Porisms, 18, 32—35, 37, 121–125, 210, Poselger, 55, 120, 124 n. Powers, additive and multiplicative evolution of, 70–71, 150—151 Progression, arithmetical, summation of, 239-240 πρότασις and πρόβλημα, 34 Ptolemy, Claudius, 9 Quadratic equation, solution of, 90- Radix, 68 Ramus, Peter, 10, 14, 15 Reduction of determinate equations, 29, 149-150 Regiomontanus, Joannes, 2, 20, 21, 22, 23, 42, 46, 78 Reimer, 32 Relati, 71 Res, 68 Riccati, Vincenzo, 27 n. Right-angled triangle: formation of, in rational numbers, 115, 141, 142; use of, 115, 127, 128, 155, 156; examples, APPENDIX, especially Book VI. pin of Nikomachos, 151 Rodet, L., 29 n., 59, 60, 61, 62, 75—76, 91 n., 92, 134, 151, 155 Rosen, editor of Mohammed ibn Mūsā, q. v. Salmasius, Claudius, 19 n., 224 Series, arithmetical; summation of, 239-240 shai, 150 66 Side-numbers," 142 Simultaneous equations, how treated by Diophantos, 80, 89, 113, 140 Sirmondus, Jacobus, 19 n., 20 Square root, how expressed by Diophantos, 93 n. Stevin, 3, 55 Struve, Dr J. and Dr K. L., 142 n. Subsidiary problems, 81, 86; examples of, 97, 110, 111 Subtraction, Diophantos' symbol for, 66 n., 71-73; Tartaglia's, 78 n.; Bombelli's, 45 Suidas, 1, 8, 9, 10, 11, 12, 13, 45 CAMBRIDGE: PRINTED BY C. J. CLAY, M.A. AND SON, AT THE UNIVERSITY PRESS. |