HISTORY OF MATHEMATICS

David Eugene Smith

VOLUME

I GENERAL SURVEY OF T H E HISTORY OF

ELEMENTARY MATHEMATICS

DOVER PUBLICATIONS, INC. NEW YORK

CONTENTS CHAPTER PAGI:

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . xiii

PRONUNCIATION. TRANSLITERATION. AND SPELLING OF

PROPER NAMES . . . . . . . . . . . . . . . . nvii

I . PREHISTORIC MATHEDlATICS

I . IN THE BEGINNING . . . . 2 . PRIMITIYE COUNTING . . . 3 . GEOMETRIC ORNAMENT . . 4 . MYSTICISM . . . . . .

I1 . THE HISTORIC PERIOD DOWN TO 1000 B.C. . . . . . . zo

I . GENERAL VIEW . . . . . . . . . . . . . . . . zo

2 . CHINA . . . . . . . . . . . . . . . . . . . z z

j . INDIA . . . . . . . . 33

4 . BABYLOS . . . . . . . . . . 35

j . EGYPT . . . . . . . . . . . . . 41

. . . . . . . 111 . THE PERIOD FROM 1000 B.C. TO 300 B.C. 54

. . . . . . . . . . . . . I THE OCCIDENT IN GENERAL 54

2 . THE GREEKS . . . . . . . . . . . . . . . . . 55 . . . . . . . . . . 3 ORIGINS OF GREEK MATHEMATICS 63

4 . FROM PYTHAGORAS TO PLATO . . . . . . . . . . . 69 . . . . . . . . 5 . INFLUENCE OF PLATO AND ARISTOTLE 87

6 . THE ORIENT . . . . . . . . . . . . . . 95

CONTENTS

CIIAPTER PAGE

IV . THE PERIOD FROM 300 B.C. TO 500 A.D. . . . . . . . I01

. . . . . . . . . . . r . THE SCHOOL OF ALEXANDRIA 102

. . . . . . . . . . . . . . . . . . . 2 . EUCLID 103

. . . . . . . . . . 3 . ERATOSTHENES AND ARCHIMEDES 108

4 . APOLLONIUS AND HIS SUCCESSORS . . . 116

5 . PERIOD OF MENELAUS . . . . . . . . . . 125

6 . PTOLEMY AND HIS SUCCESSORS . . . . . . . 130

7 . DIOPHANTUS AND HIS SUCCESSORS . . . . . . 133

8 . THE ORIENT . . . . . . . . . . . 138

V . THE PERIOD FROM 500 TO 1OOO

. . . V1 . THE OCCIDENT FROM lOOO TO 1500

I . CHRISTIAN EUROPE FROM 1000 TO I200 . . . . I94

. . . . . . . . 2 . ORIENTAL CIVILIZATION IN THE WEST 105

. . . . . . . 3 . CHRISTIAN EUROPE FROM 1200 TO 1300 211

. . . . . . . 4 . CHRISTIAN EUROPE FROM 1300 TO 1400 230

5 . CHRISTIAN EUROPE PROM I400 TO I500 . . . 242

TOPICS FOR DISCUSSION

CONTENTS CHAPTER

V11 . THE ORIENT FROM 1OOO TO 1500 . . .

TOPICS FOR DISCUSSION

V111 . THE SIXTEENTH CENTURY . I . GENERAL CONDITIONS . . . 2 . ITALY . . . . . . . 3 . FRANCE . . . . . . 4 . ENGLAND . . . . . 5 . GERMANY . . . . . . . 6 . THE NETHERLANDS . . . . 7 . SPNN . . . . . . . . . 8 . OTHER EUROPEAN COUNTR~ES . . 9 . THE ORIENT . . . . . . . .

K O . THE NEW WORLD . . . . TOPICS FOR DISCUSSION . .

IX . THE SEVENTEENTH CENTURY . . I . GENERAL CONDITIONS . . . 2 . ITALY . . . . . . . . .

j . FRANCE . . . . . .

4 . GREAT BRITNN . . . 5 . GERMANY . . . . . . . 6 . THE NETHERLAUDS . . . . . . 7 . OTHER EUROPEAN COUNTIUES . .

8 . THE ORIENT . . . . . . TOPICS FOR DISCUSSION . .

xii CONTENTS

<;BAi'TER I.A<ili

X . THE EIGHTEENTH CENTURY AND AFTER . . 444

I . GENERAL CONDITIONS . . . . . . . . . . . . . 444

. . . . . . . . . . . . . . . 2 . GREAT BRITAIN 446

3 . FRANCE . . . . . . . . . 470

4 . GERMANY . . . . . . . . . 501

5 . ITALY . . . . . . . . . . j11

6 . SWITZERLAND . . . . . . . . . . 519

1 . OTHER EUROPEAN COUNTRIES . . . . 526

. . . . . . . . 8 UNITED STATES . 531

. . . . . . . . . . . g THE ORIENT . . 533

10 . THE HISTORIANS OF MATHEMATICS . . . . 539

TOPICS FOR DISCUSSION . . . . . . 547

CHRONOLOGICAL TABLE

INDEX . . . . . .

INDEX

Since ilnportvnt nanles are oiten mentioned many tinier in the text, olily such page reierences hare been given as are likely to be of considerable value to lhe redder, the first ieierence 311~1. n proper name being to tlte bioglaphical note in case one is civeo. Uibliagrapllical references, in general, give only the page an which a book or essay is hrst ~n~~nlioned, and an this paw the full tilie appears, together with the abridged iorm rubs~uentiy uled. In arranzing the \yorrli and nnzars alphabetically, 5.. d. and ii are taken as if written se, oe, and ue respectively. The prefix MC is indexed under Mac.

.$.%hmesu. See Ahmes .Adriaen Anthaniszaon (c. 1 6 2 0 ) ~ 340 Aa-user-Ri, q i Adriaen Metius (c. 16201, 340 Abacus, 40, r41 Adrianus. See Roomen and Adriaen 'Abbis. See Jauhnri ~Esop, 186 Abhasides. xbi Aethelhard. See Adclard Abbo of Flcury (c .qSol , 190, 195 Aethelstan (c. 9251, 187 Abbot Adrian, 185 Africanus, Sextus Julius (c. z z o ) . 132 hbbott , W. C., 105 Agatharchus (c.470 e.c.1, 79, I19 Abdallih. Sec Ibn al-Y3simin hgnesi. M .G . , (c. 177a), 519 Abdera, 59, 61 A l y c d ibn 'AbdalBh al-Mer\~ari ( r . Abel. N. H. (c. 1 8 ? j l , 527 8701, 174 Abenbeder (c. 13th ccnturyl, 2 1 1 Alnned ibn 'Abdallih ihn 'Ornar (c. Abraham bar Chiia ( < . ~ ~ i o l , 206, 10501, a05

2.31 Ahrncd ibn al-Taiyib (c. 8901, 174 Abrahum ben Ezra (c. ~ i q o l , 207, 170, Ahmed ibn Di'iid (c.890), I74

350 Ahmed ibn Mohammed (al-Taiyib) Abraham Judeus (c. 1120). 206 (c.890), I74 A110 'Ali al-Chaiyit (c. 82 51, zoq Al~med ibn Mohammed ibn 'ImHd. SW Ahii Bckr Mohnmmcd. SE(. al- l . l~~:Lr, Ihn al-Hi'irn

al-l<arlihi Al!med ibn Mohammed ihn 'O!niRt~. AbG Ja'fnr al-IEhBzin (c.9601, 1;s See Albanna Abfl Kimil Shoji (c.sao), 177 Ahmed ibn Rajeb (c. 14251, 289 AbWl-Faradsh (c. q 8 i J , I;? , . \ l~mcd ibn \'Gsuf (c. 9001, 173 AbG'lLQ3sim. Set al-Mnjrt!, :\hmcs ( c , rcsa s .c .1, 47. qs AbWl-5alt l < . IIOO), 20b 4id;i Ammci ( c . 17801, 537 Abil'l-Taiyib ( r . 8501, 1 7 2 Airy, G. B. (c. 18501, 469 AllWl-Wefi (c. sso l . 1;s Ajima Chokuyen (c. 17801, 538 Abfi 'Otmin. S C F Sahl ibn Bishr hkhmim, 19, Abii YahyB (c. 7751, 168 Akkad, 37 Abfl Zakariyi. See AbG Bekr al-'Abbis. See Jauhari Academy, Plato's, 88 al-ArjBni (c. 8501, I76 Achilles problem, i 8 .4lasia, C., 499 Adam, C., 371, 375 al-Astoriibi (c .830) , l69 Adams, J . C. ( c . 1 8 j 0 ) , 469 al-Bn'albcki. Sec Qos!il Adelard of Bvlh (c. ~ x z o ) . 203 .4lbanna (c . r p o ) , 211 AdCmar. Monk ( r . 1o2j1, 186 Albategnius ( r . 9 ~ 0 1 , 175, zor Adrain, R. (c. 18081. 532, 502 al-Batriq (c. 7901, 168 Adriaan. See Adriacn :,l-Batlini. See Albategnius Adriacn Adriarnsroun (c. 16co1, 340 All;crl. See Albertus

Albertus Magnus (c. r z ~ o ) , 228 Albertus de Saxania (c. 1365), 242 Alb&rani (c. l ow) , 285, 145, 153, 157 Aibumasar (c.SSo), 174 al-Carsi (c. 1375), 241 al-Chaiyit (c. 825), a09 Alchindi (al-Kindi) (c. 860), 171, 174 Alcuin (c. 775), 185 Aldhelm, 185 al-Dimishqi. See Sa'id ibn Ya'qfib ai-Dinavari (c. 88o), 174 Alexander the Great (c. 335 B.c.), 92.

93. 1 0 2 , 144 Alexandre de Viiledieu (c. 1aq.z). a16 Alexandria, 59, 61, rot, 190 al-Fadl. See al-Nairizi al-Farad; (c. 9101, 192 ill-FargPni. See Alfraganus a l -F&dbi ( c . oaol. I?< ~~ - ,~~ -- . , .- al-FazlZri (c. 7731, 168 Alionsine Tables (c. 1 2 ~ 0 ) . az8, aro,

138, 259 Alfonso X, el Sabio, 228 Alfrasanus (c. 81,). 170. zoo ~ - ~ - ~ .-.. ~~~ ,~ ~ " " . , Alfred the Great (c. 88oj, 187 Algebra, 48, 62, 106, 1x4, 134, 158, 170,

177, 1"i, 210, 273, 278,28413m,311, 310, 328

Algorism (algorithm), 170, 2 2 2 , 125, 226, 138, 239, 160

al-Baitam of Basra (c. I-), 175 ai-Hajjaj ibn YOsuf (c. 8201, 176 Alhakem I1 (c. 970). I92 al-HarrPni. See Ibrihim ibn Hilai al-Gssan ibn al-Basan. See al-HaiQm al-Hasan ihn 'Obeidallsb (c. 925), 176 al-VassHr, Mohammed ibn 'AbdallHh

(C.1175?), 210 , 209 Alhazen. See al-Baitam of Basra al-Himsi (c. 880). 176 al-eosein, ibn sin&. S e e Avicenna 'Ali ibn Abi Sa'id. See Ibn YGnis 'Ali ibn Ahmed, al-Nasavi (c. X O Z ~ ) ,

285 'Ali ibn IbrPhim. See Ibn al-ShPtir 'Ali ibn Mohammed. See al-QalasAdf al-Jauhari. Sec Jauhari al-JorjPni (c. loon), 174 ai-Karkhi (c. 1020). 28Z

ai-KhPzin (c. s o ) , 175 .I-KhowPrirmi (<.8z5), 170, 168, 203,

329 al-Kindi. Sue Alchindi al-Kushi. See al-Kashi Allen, H. J., 25

Anthemius (c. 5251, 191 Antilogarithms, 433 Antinoopolis (Antinoc), 59, 61, 126 Anti~hon (c.ato 8.c.). &

Apameia, 59, 61 Apepa I, 47 Apianus, P. (c. I S Z ~ ) , 333 Apolloniur (c. a25 B.C.), xr6, 182, 193,

302, 406; Arab translators of, 172 Appuleius (c. ISO), 71

INDEX

Apuleius (c. ISO), 71 Aquitania, 59, 60 Arab achievements, 189 Arab writers. 2x0, 283 Arabia, 283 Arabic influence in China, ,149 Arabic numerals. Sec Hlndu-Arabic

numerals AragO, F. (c. 1840)~ 490! 494 Araki Hikosbir6 Sonyel (c. 1690). 536 Aramcans, 39, 99 Aratus (c. 270 B.c.), 92 Arborat. L. (c. 1800). So0

Arcerius, J. (c. 1600). 183 Archibald, R. C., 107 Archilochus (c. 680 6.C.). 6a ~rehimedes (c. 225 B.C.), 1i1, 302 Archimedes, cubic of, 118, 1 2 2 , I71 Archippus, 81 Architecture, 17 Archytas ( c . 4 ~ B.c.), 73. 84 Area, 40, 163. See also Circle, Triangle,

Ouadrilateral, Trapezium ~ -

Areiarius, 113 Arendt, 23, 24 Aretinus (c. 1025), 197 Argand, J. R. (c. 18101, 500 Arima Raid6 (c. 1760), 536, 537 Aristaeus (c.320 B.C.), 94 Aristarchus (c. 260 B.C.), 107, 30Z Aristotle (c. 340 B.C.), 93 Aristoxcnes (c. 350 %C.), 74 Arithmetic, 57, 58, 66, 89, 128, 129,

158, 335 Arithmetic in the Five Classics, r jo Arilbmelic in Ninc Sections. Sec K'irr-

ch'nng Arithmetic complement, 394 Arithmetic series, 155 AriHni (c. 850), 176 Arjiza, 288 Amaldo de Villa Nova (c. 1275)~ 229 Arnauld, A. (c. 1650), 386 Arnauld de Villeneuve (c. 127$), 229 Ameth. A. (c. 1840). 542 Amold, Sir E., 98 Amsprger, W'.,~soz Aronhold, S. H. (c. 1880), 511 Ars Ma~na. m? " ~-, ~, . ~ r t ~ b a s d a . See Rhabdas Artillery science, 298 Kryabbata the Elder ( e . s ~ o l , 153. - rsa, '54, I55 Aryabhata the Younger. 156 ,&yrylrbba$iyn (Aryobha!iyam), 155

&ydi!nsotn, 155 Ascham, R. (c. 1550)~ 318 Asdepias of Tralles (c. 635), 191 Assyha, 35, 39, 99, 146 Astorlkbi, al- (c. 830), l69 Astrolabe, 91, 169, 196, 197 Astrology, 39, loo, 146, 160, 218, 220,

1 2 1 , 132 Astronomical instruments, oldest, 46 Astronomy, 17. 23, 37. 39, 67. 83. 95,

107, 118, 143, 158, e t passrm Athelhard. Sec Adelard Athelston (c. 92j), 187 Athens, 59, 61, 87 Atomic theory, 80 Auhrev. T.. 1 2 1 ~ - - ~ ~ ,, . . Augrim, 170 August, E. F. (c. rSjo), 5 ~ r Augustine of Canterbury

185, !87 August~nc of Hippo (c. 400), Aurispa (c. rqaa), 143 AurdehnungJeh*e, $07, 462 Austria, 255 AutolyNS (C. 330 B.C.), 94, 302 Avanzini. G.. a 1

Averroes (c . 11751, 101 .4r,icmna (c. 102pl, 165 Awaysma. Srr Ogania .\vmar. Monk (c. lo? r l . I N r s

Baba Nobutake (c. 17oo), 536 Babbage, C. (c. 1840), 460 Babbage, H. P., 460 Babrius (c. gd century), 186 Babylon. 35 Babylonia, 35, 37, 39, 1- Bach. 1. N.. I88 ~achhh;i, C. C. (c.161r), 370, 133 Bachuone, Amald (c. 1275). 2 2 0

Bacon, Roger (c. 1250). 1 2 2 , 8 1 Bagdad, 167, 17% 177, 283 Baker, H. (c.I568), 3ar Baker, M., 515 Bakhshali manuscript, 164 Balbus (c.xw), rzs Baldi. B. (c. ,600). <W. 10s

~ ~ . . . Ball, R. S. (c. 19m), 470 Ball, W. W. Rouse, xi", 69, .3Xr, ,306,

40% 448 Baltzer, R. (c. 1860), $46 Bamberg arithmetic (1482), 360 Bamboo rods, 96, 141 Bapu Drva Sastri, r 4 j

UEX

Baraniccki, M , A., 346 Barbicri, M,, 70 Barbosa, 264 Bar Hebrzeus (c. I Z ~ O ) , 188 Barlaam ( c . ~ ? ? o ) . 212

Barnard. F. P., 184 Bzrocius, F. (c. 1580). 302 Barmzi, F. (c. 1580). 302 Barreme. F. (c. 1680). 387 Barrow, I. (c. 16701, 306 Barsotti, G., S42 Barter, 2 2 Bartoli, C. (c. ISSO), 303. ,308 Bartolomeo da Parma (c . 1z97), 220 Barton, G. A., 38 Basingstoke, John of ( c . 1240), 2 2 2

Batriq (c. 'loo), 168 Battsglini, G. (c. 18801, 518 Batthni. Sel Albategnius Battierius, J. J., 423 Bauer, W., 69 Baumgartncr, A., 76 Baur, L., 2 2 2

Bavcr. J . W. (17041. 157

Beldamandi (c. ~ g o ) , 246 Belgium, 526. Sec olro Netherlands Bell. See Schall von Bell Bellavitis, G. (c. 1850), 5r7 Belli, S. (c. 1570), 304 Beltrami, E. (c. 1880). 518 Ben. See Ibn Benares, 154 Benedetti, G. (c. 1j701. 302 Benedetto da Firenre (c. 1360), 246 Bcncdict. See Benedctto, Benedictus Benedict, St. (c. 520). 244 Benedictus. See Bencdctto, Bcncdict Renedictus Accolytus (c .z077) , 198 Benedictus Herbestus (c. 1 j6o), 346 Benese, R. de (c. 15651, 322 Ben Ezra. See Abraham ben Ezra Ben? M&% (c. 870), 171 Ben Mask. See al-Klrowirizmi Benay Kumar Sarkar, I53 Bensaude, J., 206, 349 Berkeley, G. (c. 17401, 469 Berlet, B., 337

Rrrnclinus ( r . xozo), l97 Bernauili, Christoph (c. r8qo1, 433 Bernoulli, Daniel ( I ) (c. 175a), 43' Bernoulli, Daniel (11) (c. 179o), 432 Bernoulli, Jacqucs ( I ) (c.1690), $27.

INDEX 575

Brouncker, W. (c. 16601, 410 Browne. G. F.. 184. 186 Browning, R., 207~ BluSUla% H., 425 Brunncr. K.. 10

goon i c . i s o B.c.), 84 Bryte, Walter (c. 1360)~ 137 Blibnov, N., 195 Buddha. 98, 154 Buddhism, 143. 151 Budge, E. A. W., 49 Burgi, J. (c. 1600), 338, 433 BUrk, A., 98 Buttikoffer, J., 13 Buaia. zrs

Bungus. See Bongus Burgess, E., 145 Burkhardt. H.. <16 Burlaus. see ~ L r l e v Burleigh. Sec ~ u r l i y Burley, Walter (c. 1325), 236 Bury, J. B., a43 Bussev. W. H.. 302. ,381 . - . - Buted (Buteon), J. (c. 1515)~ 311 Buxerius. See Boissihre Byrhtferth (c. I-), 196 Bvzantium. so. 61. 220. See abo Con-

stantinopll; -'

Cabala, a07 CadL, 59, 60 C a r (c.46 B.c.). 122 . . . . Cairo, 191 Caiori, F., CV, 78, 387,392,394, 531 Caland~l (Calandrus, Calender) (c.

1491), 2549 155 Calculus, 430, 439, 448. Sec also

Newton, Leihniz, Cavalieri, Barrow Calendar, 37, 42, r w , ran, 138, r40,

151, et Passim Calendrini, L. (c. 1740). 520

Cambyses (c .515 % C . ) , 71 Cameranus, J. (c. 1540). 332 C a m m u s (c. 1160). 218 ~ a n i c c i , R . ( c . 1380j, 131 Candale. Sec Foix CandoUe, A. de, 426 Canon Paschalis, 138. See alto Calendsl Cantor, G. (c. woo), 510

576 INDEX

Cantor,M. (c.1900),5.$4, xi", 14,98,183 Capella (c. 460), 183 Capes, W. W., 185 Caphanton, J. (c. 1430), 263 Cardan, H. (or J.) (c. 15151. 295. Sec

alro Cardano Cardana, F. (c. I~CO), 224, 196. See

also Cardan Carette, A. M,, 516 Caritat. See Condorcet Carmen de Algorirmo, 126 Carnat, L. N. M. (c. 18001, 494 Caron, F. (c. 16541, 442 Carpini, Fra Plan0 (c. 1246), 268 Carrara, B., 195 Carsi. Sec Carsono Carsono, J. (c.1375)~ 241 Casorati, F. (c. 1880), 518 Cassini, C. F., de Thury (c. 1756). 369 Cassini, G. D. (J. D.) (c. 16711, 369 Casini, Jacques (c. 1725), 369 Cassini, J. D., de Thury (c. 1800), 370 Cassini family, 368 Cassiodorus (Cassiodorius) (c. 520)~ 180 Casting out nines. See Nines CasweU, J . (c. r69o), 413 Cataldi, P. A. (c. IS~O), 303 Catenary, 424 Cattaldi. See Cataldi Cauchy, A. L. (c. 1830), 496 Caussinus, N., 235 Cavalieri, B. (c. 1635), 362, 418 Caxton, 314 Cayley, A. (c. 1870), 465 Cecco d' Ascoli (c. qao), 231 Celtes. C.. 180 ~ensoknus (l. 238), 131 Ceulen. See Ludolf Ceva, G. (c. 1700)~ 5rr Ceva, T. (c. I~CO), 5rr Chabas. M. F.. CO Chaignkt, A. ~ d : 69 Chaiyit (c. 8251, 209 Chalcedon, 59, 6r Chalds, 59, 6r Chaldea, 35, 39, 100,146 Chane~. See Ch'ang, =fro Chang Ch'i-mei (c.z616), 270 Ch'ang ch'un (c. ram), 168 Ch'ang ch'un-ch'ing (c. loo), 141

' Ch 'an~ H o n ~ (c. I*<). 1a1 Ch'ang K'iG (ad &ntuiy), 140 Ch'ang K'iu-kien (c. 575), 150, 267 Ch'ang K'iu-kien Suan-king, 150, 267 Ch'anz-ti (c. 12101. 268

Chang Tsu-nan, 534 Charlemagne (c. 7801, 185 Charles, E., 2 2 4 Chasles, M. (c: 1850), 498, 202, 544 Chastelet. See Chitelet ChStelet, Mm= du (c. 1745), 477 Chaucer, 160. 170 Chau J"-kui, ib7 Ch'Zn Chin-mo (c. 1650), 436 Ch'en Shih-jen (c. 1715), 535 Ch'hg Kiang Chen (c. sag a.c.), 139 Ch'eng Tai-wei (c. 10.3). ?<z - . - . . - - Chiarino, Geordb (c. 1481), 249 Chia-lsri (sexagesimals), 24 Chiia. See Ahraham bar Chiia Chiiia. See Ahraham bar Chiia

~ ~~

Ch'ilku Sum-king, r5r Child, J . M., 398 417, 418 Ch'in Dynasty, 138 China, 22, 96, 138, 148, 152, 166, 351, 435. 534

Chinghh Khan, 268, 287 Ch'in Kiu-shao (c. 1250)~ 269 Chios, 59, 61 Chiu-chi-li, 149 Chiung Lin-tai, 534 Chokuyen. Sec Ajima Ch'Bn Hua (c. rose), 266 Ch'6n I. 1 ~ 0

Ch'on iui" (c. 535). 150 Chords, table of, 119, 127, 131, 145 Chou. See Shu Ch6u K'ii-fei (c. 1178), 267 Chiru-Kung (c. 1105 B.c.), 31, 32 Chdu-pei Saon-kina, ao, ~ar. ~ r z

Chnzen. See M&$ Cicero, 84, 88, rr5 Cirde, 40, 79, 84, 92, 98, 139, 197, 236, 242; segment of, 139. 164

Circumference of the earth, 110 Ciruelo, P. S. (c. 1505). 344 Cissoid, 118, 424 Cities,ancient mathematical, 5941,154 Clairaut, A. C. (c. 1760), 475 Clairaut, J. B. (c. 1740), 475 Clairaut family, 475 Claudius. Sce Ptolemy, C.

Claudius, emperor, 124 Clavius. C. (c. 1583), 334 Clazomene, 59, 61 Clebsch, R. F. A. (c.1870), 511, 505 Cleomedes (c.40 B.c.), 122, 118 Clepsydra, 69 Clichtoveus, J. (c. ISM), 342 Cliiord, W. K. (c. 1870). 467 Cnidus, 59, 61 Cocker. E. (c. 167o), 415 Codev Arcerionus, 183 Cohen, B., 346 Coi. See Zuanne Coins, 56, 96, I40 Colebrooke, H. T., 144. 180 Colla. See Zuanne da Coi Colson, J., 404 Columella (c. zS), 123

Crafte 01 Nombryng ( c . u r n ) , 238 Cramer, F., 69 Cramer, G. (c. 1740). 520 Crawford, John, 14 Crawford, M., 180 Crelle, A. L. (c. 1820), 506 Cremona, Jacob of. See Jacob Cremona, L. (c. 18801, 517 Crete, 52, 59, 61 Cribrum (sieve), 109 Craker, J., 400 Cromberger, J., 354 Crotona (Croton), 59, 61, 7'2 Crausaz, J. P. (c. 1720), S19 Crouzas. See Crouraz Cube, duplication of, 83, 85, rr8, 136 Cubes, tables of, 40 Cubic eauation, 114. 134, 151, 294,

Comirato, 513 Commandino, F. (c. ISSO), 301, 170 Commercial mathematics, 49, 56 Compass, 97, 143 Compasses, geometry of the, 30% 516;

single opening of the, 301 Computus, 138. See also Calendar Conant, L. L., 14 Canchoid, 118, 171, 387 Condorcet, A. N. C., Marquis de (c.

1780). 481, 521 Confucius 24, 70 Conic secfions, 92, 116, 331 Conon (c. 260 B.C.), 107 Conrad von Jungingen (c.1400), 241.

Sec also Chunrad Constantinople, 59, 61, 190, 229, 130,

233, 249 Constellations, 18, 91 Continued fractions, 156, 303 Continuity, 93, 416 Contractus. See Hermannus Convergence, 497 Coordinates, 116, 129, 375, 378, 389 Copernicus (c. xsao), 346, 108 Coppernicus. See Copernicus Cordier, H., a5 cartes, 353 C m . See C o s Cosecant. 175 Cosmic figures, z Cos, 328,~320 Cossali, P. (c. I ~ O O ) , 541, 215 Cossic. See C o s Cotes, R. (C. 1710), 447,402 Counting, 6; scales of, 9, 141 Cousin, V., 137. 37s CoUtlIrat, L. (C. 1910), 500

~urricuium, 'medie;al, a14 Curtze, E. L. W. M. (c. 18801, 546,

206 Curves, higher plane, 136, 327; of

descent. 424. See also Cissoid and other name;

Cusa, Nicholas (c. 1450)~ 258 Cycloid, a59, 366, 385, 414 CYP,NS, 59, 61, 86 CYZICUS, 59, 61

INDEX

Delatore, A. (c. 1489)~ 264 Delatte,,A., 69 Demacrltus (c. 400 B.c.), So De Moivre, A. (c. 1 / 2 0 ) , 450 De Montgomery, J. E . G., 185 De Moman, A. (c. I ~ S O ) , 462, 103,

(C. 1490), 254 Domitius. See Ulpianus Domninus of Larissa (c.450), 136 Dozen. 12

Duality, '93 Du Bois-Reymond, P. (c. r880), 511 Du Boulay, 142 Dudley, l., 452 Diiker, H., zoo Direr, A. (c.z5ro), 316 Diix, J. M,, 258 Dubem, P. (c. 1900)~ 500, 75, 194 Duillier. See Fatip

Dupin, C. (c. 1830), 500, 490 Duplication of the cube, 83, 85, 118,

136 Dupuis, J., 129 D ~ P U Y , P., 498 Dusan, Stephen, 241 Dutt, R. C., 35

c, transcendence of, $00 Earth, spheridty of, 75, 81, 157;

measure of, 109 East and West, intercourse between,

140, 143, 148, 167, 4 5 , 442 Easter, 1.38. See also Calendar

Erasmue (c. 1 5 ~ 5 ) ~ 395 Eratosthenes (c. 230 B.c.). 108

INDEX

Erlendsson, Hauk (c. 1300), 240 Estaples. See Faber $taples. See Faber Euclcides. See Euclid Euclid of Alexandria (c.300 &C.), 103.

169, 182, 187, 201, 203, 250, 951, 293, 302, 304, 313, et passim; Arab translators oi. 168. 160. 171. 176, ~ ~~

Tor ; bibliog;a'phy, .?a9 Eudid of Megara, 88, 105 Euctemon (c.232 B.C.), 83 Eudemus (c. 335 B.C.), 94, 68 Eudonus (c.370 B.C.), 91% 73 Euler. 1. A. (c. I77<), <24 Euler, i. (c. 1750),-52a- Euler's Equation, 522 Eutocius (c. 560), 182 Evolutes, 424 Exhaustion, method of, 84, 91 Exponents, fractional, 239, 408; nega-

tive, 408

Faber Stapulensis (c. r50c), 307. I99 Fabricius. J. A., 85 Facia (Faccia). S?e Fatio Fadl. See al-Nairizi Fagnano, G. F. (c. 1765), 515 Fagnana di Fagnani. G. C. (c. 1/20),

514 Fa-hidn (c.400), 143, '54 Faizi. See Fyzi I;nkh.i. 286 False ~ & Z o n , 33, 216 Fan China-fu, 534 Faradi (cyqro);;iz Farkini. See Alfraganus Fir r ib i (c. 9401, 175 Fatio de Duillier. N. (c . 1700). S19 Faulhaber, J. (c.1620)~ 418 Favaro, A.,48, 299. 362, 364, 366 Favorinus (c. 1x51, 75 FarPri ( L . 7001. 168 - ,~ ., . . Federici, D. hr., 249 Federigo of Mantefeltro, 243 Feilberg, H. F., 14 Feizi. See Fyzi Feliciano da Lazerio (c. l j zo ) , 306 Fermat. P. de lc.163q). .?7i, I ?? -- . . erm mat: S. (c. ;679), 378 Fernel (Fcrnelius), J. (c. 1.53 51, 508 Ferrara. See Ferrari, L. ( Ferro (Ferri.

Domenica C. 1545). 300 Ferreo, Ferreus) ( r - . I ice). . .

295 Fibonacci, Leonardo (c. 1202I, 214, 206 Fibonacci series, 217

Ficquet, 419 Figulus, P. Nigidius (c. 60 KC.), 122

Figura cota, I 72 Figurate numbers, ~ z g Fihrist, Kitrib al- (Book of Lirtsl, 177 Finsus. See Fine Fine, Oronce (c. I525), 308 Fineus. See Fine Finger reckoning, 185, 235 Fingers in counting, 10 Finke, T. (Fink, Finck, Finchiusl

(c. 1583). 348 Fior, Antonio Maria (c. 15061, 295 Firmiani, 299 Fiskc, T. S., 531 Fitzgerald, E., 286 Fitrstephcn (c. 1180), 204 Five, scalc of, 9 Flamsteed, J. (c. 169o), 405 Fleet, J. F.. 155 Fleming, William (c. 12501, zzq Fleury, Claude, zz8 Floridus. See Fior Flor (Fibonacci) , 217 Fluxions, Newton's, 404. See also

Calculus Foix-Candale (c. 15 501, 309 Formdel, P. (c. r570), 313 Fortoliu, ( r . rogil . ~ g d Fortunalac insular, 1.30 Fourier, J. t r . rxro., 5ce Fraction,, Babblun. ?R. 1 , China. - . . .

150; cantinuhd, 156, 303, q r r ; deci:

eesimal. 14, 41. I IQ. 1.11. 132 ; unit,

470 Franccschi, Pietro ( r . r475), 247 Francesco di Simone Stabili (c. 1.3oo).

231 Franccsca dal Sole. See Sole Franchini, P. (c. 18ro), 542 Franco of Libge (c. 10661, 197 Frankland. W. B.. 103

Fraser, J., 14 Frarer. R. W., 154 Frederick the Great, 473, 478, 483, 501 Frkniclc dc Bessy, B. (c. 164o), 385 Frezicr, A. F. (C. 1740)~ 472 Friedlcin, G., 137, 178, 195 Frisch. 416 Frisi, P , 362, 364

'DEX

Frisiua. Sce Gemma Frontinus (c, loo), 123 Fuchs, E. L. (c. 18701, 510 Fuh-hi (c. 28- B.c.), i3, 28 Fujita Sadasuke (c: 1780), 537 Fujiwara Michinon (c.115o), 273 Fues. N.. C l *

dinater Gearge. See Georgius, Georgios George of Hungary (c. =SW), 263 George of Trebizond (c. 1450), 263 Georgios Pachymeres (c. r300), 119 Georgius de Hungaria (c. ~ g o o ) , 263 Gerasa, 59, 61, 127

Gerbert (c. I-), 195 Gergonne, I. D. (c. I ~ I O ) , 495 Gerhatdt, C. I., 234 Gerland of Besan~on (c.1137), 205 Gemain, Sophie (c. 1820), 499 Germany, 216, "1, 255. 324, 416, 501 Gerson (Gerseham. Gersan~desl . See

Levi &n Gerson' Ghaligai, F. (c. 1520), 306 Gheritdi, S., 231 Gherardo Cremonenoe (of Cremona)

(C.11C0). 201. 170. 171. 172 ~ h e r a r d o ' d a ~ a b h o n e i t a (c. ZISO), . .

201 Ghetaldi, M. (c. 16w), 368 Giambattiita Bcnedetti (c. 157o), 301 Gibbon, 142 Gibbs, J. W. (c. 1885), 533 Gilcs, H. A., 23 Giles, J. A., 184 Gill, J., 317 Ginsburg, J., 166, 207 Giovanni Aurkpa (c. ~ q m ) , 243 Giovanni Battista Lanfreducci (c.

1490)~ 145 Giovanni Bianchini (c. 1450), 254 Giovanni d a Firenze (c. 1411), 145 Girard, A. (c. 1630), 423, 343 Gilikii, 156 Gitti, V., 153 Glaber, Raoul (c. 1040)~ 195 Glareanus, H. L. (c. 1535). 348 Gmiinden. Johann von (c. 14.10). 158 Gnomon, j1, 69,98 Goethals, F. V., 343 Cola, 155 Golden Section, 4, 218 Golhiscbeff, 49 Gomperz, T., 7r Gondisalvi, D., 209 Gdrla z Gdrlssteyna, G. (c. 1577)~ 346 Gottxhed, J. C., so? Goutikre, 486 Gow, J., xiv, 77 G n f , J. H. (c. 19001, 546, 525 Grammateus (c. 1535). 329 Grandi, L. G. (c. 1720). 514 Grassmann, H. G. (c. Isso), S07 Grassmann, R. (c. 1860), 507 Graves, F. P., 3x0 Gravesande. Sec Van ~'Gravesande Gray, G. J, 402 Great Britam. 184, 187. 203. 220. 135, . .

1 6 5 , 314. 387, 446 Greathead, Robcrt (c. 1140), 212 Great Pyramid, 43, 44

INDEX

Greece, 54 Greek algebra, 62 Greek Anthology, I33 Greek cities, Greek mathematics, 63 Greeks, 55; in India, 144 Grigoire. Sec Saint-Vincent Gregory, D. (c. 17001, 413 Gregory, J. (c. 1670)~ 409 Gregory, J. C., 14 Gregory XIII, 42 Griffith, F. L., 48 Groma, 124 Gromatici, I24 Grosse, H., 335 Grosseteste. See Greathead Grotefend, 36 Group theory, 499 Gruma, 124 Grunert, J. A. (c. 1850), 51' Gua de Malves, J. P. de (c. 17401, 475 Gudermann, C. (c. 18501, 510 Giintber, S., xiv, 111, 190, 234, 318:

458 Guglielmini, G. B.. 214 Guglielmo de Lunis (c. lass?), 2 2 0 Guido of Arezzo (c. 1oz8), I97 Guido Grandi (c. 1 7 2 0 ) ) 514 Guijeno. See Blasius, J. M . Guilielmus. See William, Guglielmo Guilielmus Brabantinus (Flemingus)

(C. I Z ~ O ) , 129 Guldin, P. (c. 16201, 433, I37 Gunter, E. (c. 1620), 394

Haan. Sec Bierens de Haan Yabash al-YPsib (c. 8701, 174 Hachette, J. N. P. (c. 18101, 499 Hazer. T.. 7n , . , , . Hard, J., 501 waitam, al., of Basra (c . 10001, 175 Hni-tau Suon-king, 142, 152 Haithon, 269 Hajjsj, al., ibn Yflsuf (c.820), 176 Haldane. E. S., .371 Hallam, 184

8.c.J. 38 Hankel,H. (c. 187a1,543,xiv, 289, 5 2 2 Hanseatic League, 155

Hapgood, Isabel F., 530 Hare and hound problem, 32, 187 Hariot. See Harriot Harmonic proportion, 75 Harpedonaptae, 81 yarranl. See Ibr5him ibn Hilil Harriot, T. (c. 1 6 ~ 1 , 388 Harris Papyrus, 5 2 Hartsingius, P. (c. 16541, 442 Harun al-Rashid (c. SW), 168, 149 Hasan, Jewish judge (c. 95o?), 208 Yasan, al., ibn 'ObeidallPh (c. 925),

176 Hase, H., I91 Haskins, C. H., 201, 203 H a ~ ~ i r , Mohammed ibn 'Abdallgh (c.

1175 ?), zro, 209 Hatasu. See Hatshe~sut Hatono S6ha (c. 1675). 442 Hatshepsut, queen (c. I500 n.c.1, 49 Hauk Erlendssan (c. 13001, 240 Havet, J., 195 Hawkins, J. (c. 16781, 415 Hayes, C. (c. 17041, 448.404 Heath, Sir T. L., xiv, 64, 92, 103, 111,

7 1 2 , 114, 116, 133 Hccateus (c.5171, 77, 78 Hehn, J., 14 Heiberg, J. L., 103, i r r , 114, 126, 229,

-a- Heilbranner, J. C. (c. 1740). 539, 221 Heinrich, G., 410 Heinrich von Langenstein (von Her.

sen) (C. 13651, 241 Helceph, 204 Hellmann, W., 231 Helmholtz, H . L. F. von (c. 18701, 511 Henricus. See Heinrich Henrion, D. (c. 163.31, 370 Henry, C., 204, 377 Herbertus, B. (c. 15771, 346 Hirigone, P. (c. 16341, 371 Hermann, J. (c. I 7 2 0 ) , 5 2 0

Hermann the Lame. See Hermannus Contractus

Hermannus Au$ensis. See Hermannus Cantractus

Hermannus Contractus (c. 105~1. 197, I99

Hermitc, C. (c. 18701, 500 Herodatus (c.450 6.c.) . 81 ; on division

of land, 51 Hcron (Hero) (c. 50, or possibly c.

2001, 125, $84, 302 Herschel, J . F. W. (c. 1840), 469 HCSK., L. 0. (C. 18601, 510

INDEX

ram, rasms, 453 :rams (PG-kua), 15 ibn Abi HiBI. See Him51 --

H H H H v H

See a150 Zero Hipparchus (c. 140 %.C.), 119, 9a Hippias of Elis (c.425 @.C.), 82, 91 Hippocrates of Chios (c.460 %C.), 81 Hire. See Lahire Hirth, F., 13, 140 Hirth and Rndrhill. 269

H H

ill, G. W. (C. 1 9 ~ ) ~ 531 illebrandt, A., 34 filer, E., 129 ilprecht, H. V., xv, 37, 40 imsi (c.880), 176 indu-Arabic numerals, '44, 166, 234.

-~..~~- ~, hoalenrjs. See ~oh>hes

Hock, C. Hodgson, Hoecke.

F., 195 J. (C. 1636)~ 448

See Vander Hoecke Hoernle, R., 164 Holland, 526 Sec Netherlands Holliday, F. (c. 17491, 449 H o h a n n . W. See Xvlander Hommel. F., loo Honda. Sec Fujita uonein ibn IshPq (c. 840), 176 Hook, F. W., 185 Hepital. See L'Hospital Hopkins, E. W., 7z Horace, 85 Homer, W. G. (c. 18191, 459 Homer's Method, 270, 273, 459 Wosein. See Avicenna Hospital. See L'Hospital Ho-t'u, 28 Hoiiel, 529 Hrabanus Maurus (c. 820), 188 Hrotsvitha (c.9701, 189 Hsia-hou Yang (c. 5501, 150 HsY-hou Ynnr Suan- kin^. zco Hsin Yun-lu cc. 1590). 3ia

- Hsii Kuang-ching ( c . 16oj), 304 Hsii Yiieh (c. 2501, 10 Huang-ti, emperor (c. 27W ex.) ,

31, 97 Huang-ti KYu-ch'ang, 267 Hiian-tsang (c. 640), 149, 155 H u ~ I ~ , C., 170 Huber, D., 4%

Huber, E., 38 Hudde, J. (c. 1680), 415 Hugenius. See Huygens Hui-sing (c. 5181, 148 Hulsius, L., 433 HultKh, F., !as, 136 Hume (Humlus), J. (c. 1636), Hunt, A. S., 49 Hutton, C. (c. 178a), 458, 451 Huygens, C. (c. 1670), 413 Hvde. T.. a80

Hjipatia (c. 410); 137 Hyperbola, 92, 116 Hyperbolic functions, 458 Hy~erboloid, 41q Hy'PSides (c: 18; %.c,), 119

Iamblichus (c.315). 135.69 Ibn Abi Ya'qhb al-Nadlm (c. q87), 177 Ibn al-HP'irn (c. I ~ w ) , a88 Ibn al-KStib (c. zoo), 210

Ibn al-LubOdi (c. 126o), 288 lbn al-Mejdl (c 14001, 289 Ibn al-Saflir (c. 1025), 205 Ibn al-Sal?& (c. ~ r h o ) , 286 Ibn al-ShPtir (c. 1350). 289 Ibn al-YPsirnin (c. lzoo), a88 Ibn al-ZarqUs (c. S O ~ O ) , 205 Ibn Bedr (c.13th century), zIr Ibn Man'a (c. zoo), 187 Ibn MasB. See al-KhowPrirmi Ibn RPhiweih. See al-Arjinf Ibn Ynnis (c. 1000). 175, 191 Ibn Yanis the Younger (c. I Z O O ) , 187 Ibfahim ibn Hilkl ((c. 9751, I75 I b r a i m ibn Sinin (c. 9401, 175 Ibrahim ibn YahyP (c. 10501, 205 Ibrim. sa I-hsing-(c. 727), 151 I-king, a3, 25, 142, 267 Imaginary numbem, Qar, 423, 00,

450 Imamura Chish6 (c. r639), 437, 353 Imanuel ben Jacob Bonfils, 141 Indeterminate equations, 119,150,155,

156, 158, 159, 163 India! 33, 97, 144. 152, 274, 435 Indivulbles, 93, 361, 408 Induction, 302 Infinite products, 312 Infinite series. Sec Series Infinitesimal, 416 Integral, 430 Intercoune between East and West,

140. 143, 148, 267, 0 5 , 442

INDEX 583

Invariants, 483 Isaae. See IsbPq lsaac ben Tosenh Israeli (c. 1330)s 240 ~-~ ~ ~ .. Isaac ben Saldm (c. 9301, 192 +C ben Sid (c. 1250), 210

'Is% ibn YahyP (c. m a ) . 174 Isely, L., 426 I-se-ma-yin (c. 1267), 272

Ishkq ibn Ifonein ( c . 9 ~ 1 , 172, 176 Isidorus (c. 610), 183 Isochronous curve, 428 Isocrates, 7 1 Isomura Kittoku (c. 16601, 437 Isoperimetry, 136 Italy, 214, 220, 231, 245, 294, 361, 511 Ivory, J. (c. r aw) , 469 Iwasaki Toshihisa (c. 1775). 537

Jabir ibn Aflah (c. I I ~ O ) , 206 J%bir ibn WaiyPn al-Sbfi. See Jeber Jacob. See Ya'qpb Jacob ben Machlr (c. 125o), 210 Jacob ben Nissim (c.Sm), 188 Jacob Caphanton (c. 1430). 263 Jacob Canon0 (c. 1375)~ 'I41 Jacob of Cremona (c. 1449), 147 Jamb PoEl (c. 1360), 241 Jacob, Simon (c. 1550), 338 Jacobi, C. G. J. (c. 18301, 506 Jacoli, F., 242, 366, 385 Ja'far ibn Mohammed (c.8801, '74 Tainas i Tinas). Ibr

.Ta~an,144; 151, 273, 437, 535 Jartoux, P. (c.r?ro), 534, 536 Jauhari, al. (c. 8301, I76 lean d'Estrks. 208

Joannes Pcdiasimus (c. r330), 234 Joannes Philoponus (c. 64o?), 191 Johann van Kunsperck. See Regio-

mantanus Johann von Gmiinden (c. 1430). 258 Johannes. See Joannes, Jahann, John,

Jean, Giovanni Johannes Hispalensis (Hipanensis)

(C. I I ~ O ) , 209, 170 Johannes de Lineriis (c. 1340). 138 Johannes Saxoniensis (14th century),

238 John. See Joannes, Johannes, Johann,

Jean, Giovanni John of Basingstoke (c.1240), 1 2 2 John of Beverley (c. 69o), I85 John of Luna (c. I I ~ O ) , z q , 170 John of Seville (c. I I ~ O ) , 209, r7o Tnhnmn. G.. 128 < ...~~. -.., - ~ , - ~

lanes, W., 34 Jordanus Ncmararius (of Namur, de

Saxonia) (c. 1zz5), 226, 199 JorjPni, al. (c. I-), 174 Joseph ben Wakkar (c. 1380), 24I Tosenhus Problem. 207

juan Diez. See Diez JGhann2, Sec Bar Hebrreus Junge, G., 75 Junta dos Mathematicos, 263

Kastner, A. G. (C. 1770)~ 541 Kahun, 47 R'oi-ylion Chorr-king, 151 KOakriyB, 155 Kaldi, 39, loo Kalanymos ben Kalonymos (c. q a o ) ,

jean de ~ i g n k k ( c . ,3401, 238 241 Jean de Meurs (c. 13501, 238 Kgmil, AbG (c. gm) , 1 7 7 Jebb, K. C., 260, 314. 344 Kankah (c . 766), 167, 168 Jcbb, S., 224 Kanroku, 151 Jeber (Geber, c. 770), 168 Karamzin, N. M,, 350 Jehuds ben Salornon Kahen (c. 1240), ICarlihi (6.1020), 283

209 Karpinslri, 1.. C., xv, 98, 166, 170, 177, Jehuda Verga (c. 1450), 263 238% 239, 262, 4r3 Jemshid. See al-Kashi Kashl, al. (c. I ~ J O ) , 289 Jennhiz Khan, 268, 287 Kayc, G. R., 98, 144, 145, 153, 164,

Zadeh. See Kashi jer is lem, 6 1 27.4 Jews, 172. 106, 140, 263, 346. 350 Kazi Jindoi monji, 144 Keane, A. H., 14 Joannes. Sec Johannes, Johann, John, Kelvin, Lord (c. 1880), 479

J ~ ~ " , c ; ~ . . ~ ~ ~ ; Kcm.1 ed-din ibn YGnis (c. ~zw) . 287 Jo~nn- Jw -... .. -. - ....... . - ~ - . -~~ ~

montanus K&, Joannes de Muris (c. 1350). 238 Kcrse

-. ".*..... ~~ ~- ~

.....-.. Grammaticus (c.640), 191 Kenryfi. See Miyake annm dc blulontrresio See Reeia- Kepler, J. (c. 16101, 416

H., 153 Y, J. (C. 1650), 414

INDEX

Ketensis. See Roben of Chester Keyser, C. J., 531 Khayyam, Omar (c. r r w ) , 286 Khizin (c.950), 175 Khidr (c. I-), 285 Khoradn, 172 Khorrd (c. 525). '64 Khowarirmi (c. 8 ~ 5 ) ~ 170, 168, 203,329 Khwarerm, 170 Ki-li, emperor ( c . 1 2 0 0 s.c.1, 97 Killingworth, J. (c. 1435), 261 Kind!. Sec Aichindi King, C. W., 70 Kingsley, C., 131 Kingsmill, T. W., 140 Kircher, A. (c. r65o), 422 Kirkman, T. P. (c. 1850)~ 469 KitEb oi-FihtirL (Book of Lbts), 177 Kittoku. See Isamura K'iu Ch'ang ch'un (c. rzzI), 268 K'iu-ch'ang Suan-rhu (Arithmetic in

Nine Sections), 31, 96, 14% 152 Kiu-shu, 152 Kiu-rsu, 152 Klau. Sec Clavius KIor, T. (C. 1538). 346 Kluge, F., 196 Knobel, E. B., 131, a80 Knott, C. G., 391 Knotted cords, 139 Kdbel, 1. (c. 1520), 336 Koenig, S. (c. 1750), 474 Kapke, E. R. A., 189 Konen, H., 412 Korea, 144, 151 Kosta. See QostP K6u Sh6u-king (c. I290), 272 Koval&sky, S. (c. r885), 530 Kawa. See Seki Krauss, S., 138 Kroll, W., 103 Kronecker, L. (c. 1870), 5x1 Krukovsky. See Kovalevsky Kublai Khan, 272 Kummer, E. E. (c. 185o), 507 Kushi. See al-Kashi KQshyir ibn LehbPn (c. ~ o o o ) , 176 Kuster. L., 60 Kusumapura, 153, 15s Ku!okhidyaka, 158 Kutta. W. M.. to2 ~. . ~

K'u ~ing-hsiakg(c , 1550). 351

Lachmann, K., I24 Lacouperie, A. T. de, 24, a5 Lacroix, S. F. (c. 1800), 492, 540

Ladies' Diorv. nn7 .. ... Lafon, M. A., 495 Lagny, T. F. de (c. 1710)~ 471 Lagrange, J. L. (c. 1780), 482 Laguerre, E. (c. 1880), 500 Lahire. P. de (c. 1600). l86 . . . . . Lair, j., 186 Lalande (c. 18w), 540 Lalitavbtaro, 98 Laloubtre. See Loubhre Lalouvhre. See Loubhre Lambert, J. H. (c. 177o), 480 Lamba, Ch., 261 Lame, G. (c. 184o), 5 w Landen, J. (c. 1760), 457 Landi, F., 516 Lanfreducci (c. 1490)~ 245 L a w , J., 5 2 5 Ladicea, 59, 61 Lao-Tze, 70 Laplace, P. S. (c. x w ) , 486 La-Du-tan (C. IZ67\. l 7 2

. Lamm, 39 LBta, 145 Latin mathematical vocabulary. See

Veratti Lauchen, G. J. von. See Rhaticus Lavrovsky, 350 Lax, G. (c. 151~).,345 Lazesio. Sec Feliaano Lzzarini, M,, 215 Le. See Li Leap year. See Calendar Least squares, 448, 502 Le Besgue, V. A., 214 Lebon, E., 499 Lebrira, 264 Legendre, A. M. (c. 18w), 487 Leibniz, G. W. Freiherr von (c. 1682).

4'7 Lejeune-Dirichlet. Sce Dirichlet Leland, J., 204 Ledamas (r 380 B.c.), 91 Leonardo of Cremona (c. 1415). 247 Leonardo Fibonacci (of Pba) (c. 1202),

114,206 Leonardo da Vinci (c.15ca), 294, 25.1 Lepsius, J., 480 Ledie, J., 445 Letters of the era of the gods, 144 Leucippus (c.440 -.C.), 80 Levi, B., 98 Levi ben Gerson (c. ~3301, 240 Lew. See Liu Leyboum, W. (c. 1670). 414

IND

LnBpitnl. See L'Hwpital L'Hmpital, G. F. A. de (c. 1690), 384 Lhuilier, S. A. J. (c. 18oa), 515 Lia-g I (two principles), 25 Libn abnci. See Fibonacci Ubn augnmti et diminutionis, 207 Libn embadorurn, 206 Libn pundratorum, 217 Liberal arts, 180 Libraries : Alexandrian, 103 ; early

Renaissance, a43 ; Laurentian, 243 i Vatican, 243

Libradi. 144 Libd, G. (c. 185o), xv, 545,377 Li Cbi T6'ao (c. 1605), 304 Lie, S. (c. I ~ O O ) , 517 Liebhard. See Camernrius Lieblein, J.. 45 Lietzmann, W., 69 Life, advent of, 5 Lignhres, Jean de (c. 1340), 238 Liltiuati, 276, 158 Lihwati. See LiEvati Lineriis, Johannes de (c. 1340), 238 Liouville, J. (c. 1850), 500 Li Ping (c. 250), 14% Li Sbu (c. 2700 B.c.), 24 Little, A. G., 221, 2 2 2 Little. A. 1.. 22 ~ i u - d a n g ; 15% Liu Chih (c. 289), 143 Liu Chih the Younger (c. 1360). 143 Liu Hsiao (c. PS), 141 Liu Hsing (c.66), 141 Llu Hui (c. 263), 142, 25. 267 Liu I (C. IZSO), 271 Liu Ju-hsieb (c. ISSO), 271, 172 Liveriis. See Lineriis -~ ~~~~-~ - ~

Li Yeh (c. I Z ~ O ) , 270, 535 Lobachevsky, N. I. (c.1815), 529 Loci, plane, 117; solid, 95 Lackwood, D. P,, 201 Loftus. W. K., 39 Logarithmic curve, 428 Losarithms, 338, 391, 394, 436, 433,

Longornontanus, 4rr Loamis, E. (c. 1860), 539 Loria, G., xv, 214, 343. 366, 481,

5:4 Lontus. Sce Glareanus Lo-shu, 28

LouWre, A. de la (c. 16401, 385 Laxodrome, 413 Luhbock, Sir J., 14 LubGdi, al- (c. 126o), 288 Luca di Borgo. Scc PacioLi Luca da Firenze (c. 14w), 145 Lu-S, E., 14 Luc~S, H. (C. 1640),,395 Lucasian professorsh~p, 395 Lucianur (ad century), 128 Ludolf van Ceulen (c. 1580), 330 Ludolph. See Ludolf Luke. Sec Luca Lullus, Raymundus (c. 118o), 229 Luner of Hippocrates (c. 460 B.c.),

Mabillon, J., 184 McClatchie, T., 25 MeClenan. R. B.. 217 - - ~ - ~

~ c ~ l i n t o c k , E. (c. =ago), 533 MacCullagh, J. (c. 1840), 469 Macfarlane, A. (c. 1900), 546, 461 McGee, W. J . , 14 Maclaurin, C. (c. 1740). 451 Maclaurin'r Theorem. a n MacMahon, P. A., 463'-- Magic squares, 28, 109 Magini, G. A. (c. 1595), 367 Mama Grecia. 7 1

~ a & i & k y (c. I ~ O O ) , 435 MahibhBrata, 35, 98. M$h$nl. See AlmPhad Mah.%vira. See Mahiviricirya Mahivirzic5rya (c.850), 161, 152, 154 Mahler, E., 46 Mailly, E., 526 Maimonides (c. 1175), 208 Maim, A , 381 Majrltl (c. looo), 192 Malchus the Tyrian (c.z75), I35 Malfatti, G. F. G. (c.1770). 515 Malfatti's problem, 515, 538 Malves. See Gua de Malves Mamercus, 77 MBmGn. al- (c. 820). 160 ~ a n c i n i . G.. 247. z s l ~. -

Mandurth. John ( r . Ijro,, 2 3 6 Manirrdi. Eraclilo ( r . 1720.. 512 Manfredi, Euslachio ( c . 1710,, ~ 1 1

Manfredi, G. (c. 1730), 51% Manfredania, G. B. (c. 1475), 154 Maneili. G.. (16 -~~ , ~ , . Maeu Khan. 268

Mann, A., 14 Manning, Mrs., 155 Mansion, P. (c. 18901, 546 MansOr, al- (c. 7701, 167 Mansor ibn 'Ali (c. 1000). 285 Mantovani, V., 295 Manuel. See Moschopoulua, Chry-

soloras Manzolo (Manrolino), 249 Maos, mathematical-historical, bo, 113, . .

'54 Marco Polo (c.1271), 169 Mares (Marros) (c. 1850 B.'-.), 45 Margnvita Phylosophicn, 320, 213,

214 Mariani, G. (c. 1535). 306 Mane, M. (c. 1880), xv, 54p Marinus of Ravla Neapolrs (c.485),

138 Marinus of Tyre (c. 150). 129 Marolois, S. (c. 16001, 423 Marre, A., 211, 261, 313, 3.51 Maahman, J. C., 34 Martin, T . H., 125, 129 Martin, Th., 190 Martin, W. A. P,, 31 Martinus (Martinez), J . See Blasius,

J. M. Marullo. See Mauralico

Mascheiohi; L. (c. 180o), 516 M%-shH'-ailih. See Messahala Madhi al- ( r X-). = i n . . - .~ , - - - ~ - - . , . . Maspero, H., 108 Master Nicholas (c. r250), 2t8 Masterson, T. (c. 1590), 314 Mas'iidi (c. 9501, 149 Maternus, J. Firmicus (c. 3401, 13 j Mathematia, defined, 1; elemcntary,

444 Mathematurn Rudiments quordam

(anon.), 209 Mathew. See Matteo Mabunaga Ryahitsu (c. 1730), 536 Matteo da Firenre (c. 1400), 245 Matteo Ricci (c. 16031, 303, 435 Matthaei. 0.. 241 Matthew. See Matteo Maupertuis, P. L. M. de (r.r73o),

473 Maurolim, F. (c. ISSO). 301

Maurolycus. See Mauralico Maurus, Hrabanus (c. 8201, 188 Mauthner, F., 137 Maxima and minima, 42.4 Maximus Planudes (c. 13401, 233 Maxwell, J. C. (c. 18701, 470 Meadows of Cold, 149 Mean proportionals, 83 Mkhain, P. F. A. (C. 17801, 491 Mechanics, 111, 137 Medieval curriculum, 114 Medma (Medmzusl, 59, 61, pr Megasthenes, 153, 154 Megiorini, P. (c. rs4o), a57 Meier, R., 125 Mei Wen-tin% (c. r675), 436 Melanchthon, P. (c. 15401, 331, 328 Men (c.575), 150 Mensschmian Triads, 92 Menzchmus (c. 350 e.c.), 92 Mendes, 59, 61 Mendoza, A. de, 354 Menelaus (c. ~ w ) , 126, 172, 302, 406 Menge, 103 Menher, V. (c. 1570)~ 34% Mensa Pythagarica, 129 Meray, C. (c. 1880), sw Mercator, N. (c. 1650), 434 Merejkawski, D , 294 Merian, P,, 427 Merlai. See Morley, D. Merriman, M,, 488 Memenne, M. (c. 1630), 380 Mervarrtrji, al- (c. 830), 169 Mervazi, al- (c. 860), 174 Mesopotamia, 33, 37, 99, 146, 166 Mesrahala (c. 800). 160

INDEX 587

rizmi Mohammed ibn 'Omar. al-Rizi (c. - -

12oo), 286. Se? also Abenbeder Mohammed ibn YahyH. See Avenpace Mohammed ibn Zakariyi. See Rhases Mohl, J., z5 Moivre. See De Maivre Moitzer. See Micyllus Monge, G. (c. 1800), 490 Monier-Wiiliams, M,, 153 Monmort See Montmort ..... - ~

Montalte. See Pascal Monte Regal Piedmantois (c. 1585),

314 Montgomery, J. E. G. de, 185 Montmort, P. R. de (c. I71o), 471 Montuda, J. E. (c. 1750). XV, 540 More, T. (c. 15161, 316 Morgan, M. H., 12s M6ri Kambei Shigeyoshi (c. I592), 352

Morley, Daniel (c. ~zcm), 104 Morley, F. V., 388 Morley, H., 295 Morley, S. G., 14 Morx, H. B., 140 Mortalitv table. I r r Mortet, V., 132 " M O S C ~ ~ ~ O U ~ U S (C. ISOO), 234 Moses ben Maimun. See Maimonides MOXS ben Tibbon (c. rzgo), 209, 210 Moses Kapsali, 350 Moya, J. P. de (c. 1562)~ 345 Miiller, C. F., 330 Miiller, F., 241 Miiller, Johann. See Regiomontanus Miiller, T., 327 Muhammed. See Mohammed Mullach, F. W. A. (F. G. A.), 80 Multiplication tables, 40, 58, lz9, 138,

314 Mufioz, J. (c. 1566), 345 Munyos. See Mu~ioz Murai Chfiren (c. 1765)~ 537 Muramatsu KudayO Mose~ (c. 16631,

439 Muris. See Jean de Meurs Masi ibn ShHkir (c. 8so), 171 M i i d ibn Yiinis (c. 1200) , 287 Musi:, 75, 106 Musilm ~ b n Allmed al-Leiyi (c. 9001,

192 Mydorpe, C. (c. 16301, 378 Myriad, 116, 144 Mysore, 154, 16' Mystiry of numbers, 304 Mysticism, 16, 89

Nadim (c.g87), 177 Nagl, A., 195, 239 Naixean. a86 ~a iy iz i , =l: (c. gro), 176 Nakane Genjun (c. l75o), 536 Nakane Genkei (c. 17oo), 440. 536 NBnH GhBt, I54 Naoier. T. (c. 16141, 389

NGduci , E., 182, 220 , 229, 253 Nasavi (c. 1025), 285 Nasir ed-din (c. 12<0), 287 - -. - . - Nau. F.. 288 Nau;k, 'A., 69 Nar$m ed-din Ahmed, 351 Nazif ibn Jumn (Jemen) (c. 9 8 0 ) ~

174 Neander, A., 185 Neander, M. (c. 1570), 332

INDEX

Nebuchadnerzar (c. 550 B.c.), roo Negative numbers, 159, 162 Nehhvendi (c. 820). I69 Neile, W. (c. 16651, 412 Nelli, G. P. C. de', 364 Ne-mat-re. 4s Ncthcrlands,j38, 422, 526 Neumann. See Neander Newbald. W . R.. 82 ~ e w c o m b , S. (c: 18801, 532 Newton, Sir Isaac (c. 10801, 398 Nica~a,, 59, 61 Niccolo de' Niccoli (c. 1400), 243 Nichalas. Master. zr8 ~ i c h o l a i ~ u s a ( C . 14501, 258 Nicholas Rhabdas (c. 13411, 235 Nicolas, P. (c. r700), 387 Nicole. See Oresme Nicole, F . (c. 1730), 472 Nicamachus (c. loo), 127, 179 Nicomedce (c. 180 B.c.), 1x8 Nicoteles (c. ago B.c.), *a? Nigidius. See Figulus Nilometer, 46 N i m Sections. See K'irr-rk'nng Nines, casting out, 207 Nippur, 40 Nipsus, M. Juniua (c. 1801, 131 Nissim, Jacob ben (c.800), 188 Nix, L. M. L., 172 Nobutake. Sec Baba NGldeke, T., 164 Noether, M., 463, Soil 527 Nanius. See Nunca Notker Labeo (c. ~ o o o ) . 196 Novara, D. M. (c. rqqa), 254 Norawa Teichi, ( r . 16611. dxa - , Nuffar, 40 Nugnc. See Nuaes Number and language, h Numbers, perfect, 189, 307, mystery

Of, 304 Numerals. Russian. 202; Sunlcrian, 30;

Suriar X - , . .- -, - Nunes, P. (c. r s j o ) . 348 N6iiez. See Nunrs Xiir ed-din al-Bctriiji. See Alpctragius

O'Connell, Mme F., 531 O'Creat, N. (c. 1150 )~ 204 Ocreatus. See O'Creat Odo of Cluny (c. g m ) , ~ q o Odoric, Friar (c. 1300), 27% (Enopides (c.465 B.c.), 79, 83 Oktai Khan (c. rz~o). 287

ier. T. (c. 184a), 400 L., 19s n Ibrahim al-Khayyhmi. See Khayyam layyam (c . 1 1 0 0 ) ~ 286

0meiv; See Abii'l-Salt OPP& G., 35 Optics, 106 Opuntius (c.375 B.c.], 91 Omsmc (c. 13601, 239, 199, 233 Orient. 95, 138, 350. 435, 533 Oriental mathematics. See Babylon.

Chaldea, China, India, Japan, Persia Ornament, geometric, 15 Ortega, J. (c. I S ~ Z ) , 344 Ortiz, D. (15th century), 263 Omood, W. F., 533 n thn FPI nttn - .~~. . --- - ..- O f t ~ , V. (C. 15731, 340 Oughtred, W. (c. 1630), 392 Oyama Shi,kei (c. 17281, 535

164, 198. 242, 247, 270. 275, 312, 331, 340. 4093 4'1. 43.6, 4371 536

Pachvmeres. Geore~os (c. too). zzo ~ a c i o l i (c. 14941, 3'17 - Paciualo. See Pacioli Pa-kua, cight trigrams, 25 Palibathra. I ra Pamphila, 67"- PaAca Siddhinlikd, 156 Pan K u ( c 75), r4r Paolo Dagomari, d ~ l l ' Abaco (c. 1340).

Parchment, 105 Parmt, A. (c 17101, 471 Paris. 206 ~a rnkn ides of Elea (c.460 B.c.) . 81 Paros 59, 61 Pascal, B. (c. r6 jo) , 381 Pascal's Triangle, 382, 329, 333, 537 Pastor. See Rev Pastor PStaliputra ( ~ $ o l i G G a ) , 153 Pi!aliputraka, 154 Patna, 153. 154 Paton, W. R., 133 PauliSa Siddhdntn, 145 Pauly-Wissowa, xv, 103 Peachamus. See Peckham

Peacock, G. (c. 1830), 459 Peccamus. See Peckham Peckham, John (c. 128o), 224, 296 Pediasimus (c. 1330), 234 Peepin, A. N., a6a Peet, T. E., 47, 48 Peiper, R., 198 Peirce, B. (c. 1850), 532 Peirce, C. S., 2x8 Peking, instruments at, l 7 2 Peletier (Peletarius), J. (c. 1560), 313 Pcll, J. (c. 1650), 4" Pell Equation, 160 Pellos (Pellizzati) (c. INS), a55 Pkluse. See Mange Penno, ga Perez (modern PCrez) . See Moya Pkrez, J. A. S., z r r Perga, 59, 61, 116 Pergamurn, 59, 61 Pericles (c. 444 8.c.) , 87 Peripatetic School, 03 Perito Annotio. See Cataldi Permutations, 274. See also I-king Perseus (c. 150 %C.), 1x8 Persia, 143, 164, 283, 286 Perspective, 79, 123 Pescheck, C. (c. 1720). 502 Peschel, 0. F., 14 Pestalozzi, J. H. (c. 1,776), 524 Peter. Sec Petrus, Pletro Peters, C. H. F., 131 Petrarch, 230 Petric, W. M. Flinders, 47 Petrus. See Peter, Pietro Petrus de Alliaca (c. 1400), 240 Petrus de Dacia (c. 13251, 238 Petrus de Maharncuria (c. 1265), 226 Petrus Peregrinus (c. 1265), a26 Pctrus Philomenus (c. 1325), 238 Peurbach, G. von (c. 1460), a59 --, - 7 ,

Pfaff, J. F. ( c . 181o), 510 Phaeinus (c. 432 BC.), 83 Phidiar (Pheidias) (c.443 B.c.), 87 Philippus Medmatus (c.350 B.c.), 61,

~ ~

91 Phillips, P. L., 388 Philolaus (c.425 B.c.), 81, 73, 76 Philoponus, Joannes (c. 64o?), 191 Philosophical Transactions, 259 Pi. See 71 above Picataste y Rodriguez, F., 343 Piavet, F., 195 Piedmontois. See Monte Regal Piero. See Pietm, Petrus

Pierpont, J., 445, 531 Pietro d'Abana (c. 1300), 2 2 0 Pietro Francesehi (dclla Francescal

(C. 1475)~ 247 Pithsanus. See Peckham Pitiscus, B. (c. r595), 331 P'i Yen-tsung ( c . 4401, 143 Plane numbers, 155 Planudes, Maximus (c. 1340),,233 Plato (c. 380 B.c.), 87; on anthmctic,

57, 89; on geometry, 90 Plato of Tivoli (Tiburtinus) (c. Irzo),

201, 207 Platonic number, 89 Plavfair. J.. 292 ~ l e y t e , W., so Pliny (c . ;j . 1 1 3 . 4 1 Plucker, J ( c 13:01. 505 Plumian ~,rufssrorshru. 427 .. ... Plus and minus signs, 258, 330, 341 Plutarch, 68, 88, 1;s Po81, Jacob (c. 1360), 241 Poz~endorff. T. C.. xv poggio ~ra&folini' (c. 1414), 243 Paincark. H. (c. 19m), 499 Poinsot, L. (c. 182a), 499 Poisson, S. D. (c. 18201, 495 Poland. 7n6 Polar trringle, 423 Polemarchus (4th century B.c.), 95 Polycrates, 70 Polygonal numbers, go, 119 Polyhedrons, regular, 73, 75, 95, 119 Pompeii, 59, 61 Poncelet, J. V. (c. 18301, 496 Porisms, 107 Porphyrius (c. 2751, 135 Portugal, 348 Porus. See Sporus Poseidanius ( c . loo B.c.), 118 Posidonius. See Poseidonius Poudra, N. G., 383 Poullet-Delisle, A. C. M,, 504 Predari, F., 362 Prime numbers, 109 Principia, Newton's, 402, 406, 447 Printing, origin of, 144; early, 249 Prior, 0. H., 314 Probability, 382, 428 Problems. famous and fanciful, 50, 133,

159, 162, 163, 164, 187, 207, 280 Proclus (c. 460), 137, 67, 302 Progressions, 40, rr9. 150 Projection, 79, 119 Prophatius (c. 125o), 210 Proportion, 90

INDEX

Proportion, hatmonic, 75 Fmdocimo de' Beldamandi (c. I4lo),

166 prowe, L., 347 Psammeticbus I (c.625 S.C.), 71 Psammetichus 111 (c.515 B.c.), 71 PSdlUS (C.1075), 197 Ptolemaeus. Claudius. See Ptolemy Ptolemais, '59, 61 Ptolemy, Claude (c.lSo), 130, 145,

168, 169, 179, 228, 302 Ptolemy N (Philopator), l16 Ptolemv Soter. 102

Puiveriier, 158; 280 Purbach. Sec Peurbach Putna. See Patna .--- ~ - -

Putnam, G. H., 144 Puzzles, 133 See (JIO Problems Pyramids oi Egypt, 43, 44 Pythagoras (c. 540 B.c.), 69, 254 Pythagorean numbers, 90, 97, 281 Pythagorean Theorem, 75, 30, 33, 97,

137

Qaisar ibn Abi'l-Qbim. See Ta'bif QaiasW (c. 1475). 111 Qbim. See al-Majdti Qass ( c . 9 ~ ) ~ 174 Qible (c. pm), 192 Q i w b cd-din YahyP (12th centurj),

2 9 Qorn. See Tibit Qostg ibn LDq$ al-Ba'albeki ( c . gm),

172 Quadratic equation, 134, 155, 159, 162,

280, 281 Quadmtnx, 82, 92, 136 Quadrature, 83, 197, 236, 408. See

also Circle Quadrilateral, 158, 163 Quadrivium, 180 Quarter squares, 283 Quaternions, 461 Qubtelet, L. A. J. (c. ISSO), 526, 414

Ra-&us, 47 Rabanus. Sec Hrabanus Rabbi ben Ezra. See Abraham ben

Ezra Radau, H., 37 Radix in counting, 8 Radulph of Laon (c. zras), 105 Rafaele Canacd (c. 1380), 232 U t h a (c. 1621), 435 Rahn, J. H. (c.1660), 412

Raida. Sec Arimp Rainer. Sec Gemma Ralphmn. See Raphmn Ramaka, queen, 49 Uamanujacharla, N., 274 Rambaud. A.. 178

INDEX

3037 435 Richard, C. (c. 1630)~ 370 Richard of Wallingfod (C.1330). 135 Richadson, H. K., 143 Riemann, G. F. B. (C. 1850)~ 5 d Riese, A. (c. 1518)~ 337 Rinnelberaius (Ringelbergh), J. F. (c.

1:30), 539, Rithmomachla, 198, I97 Ritzenstein. A.. 117 -..... Rixner and ~i 'bec. 199 Robert of Chester (c. I I ~ O ) , 103, 319 Robert Greathead. Sec Greathead Robert of Lincoln. See Greathead Rnberval. G. P. de (c. 1640). 385 .... .- . -~, - . .~ Robinson, L. G., 114 Roche, Estienne de la (c. 1520), 3139 161 Rockhill, W. W., I40 Rodet, L., 153, l07 Rodrinuez. See Picatoste Roettier, 401 Roger Bacon. See Bacon r oil and us (c. 1424)~ 261 Rolle, M. (c. 1700), 387 Rollin Pa~vrus . 50 & A n . >Le ~ o o m e n Romanus. See Roomen Rome, 59, 61, I10 Roomen, A. van (c. 1593)~ 339 Roots, approximations for, 184 Rooer. M.. 317 . ~ & n , F., 174 Roth, P. (C. 1610)~ 411 Rothln~f, B., 90 Rowe. l. (c. 1751)~ 448 koyai b a d to'ieometry, 91 ~ u b r o u c k (13th century), 168 Rudio, F., 84, 480, 509 Rudolff, C. (c. ISlS), 318 Rudoloh of Brunes (c. 1x44). 201 ~ u d o i f f . A., 11q Rufbni, P. (c. 1800), 515 R U I ~ of False Postion. Sec False

Position Rule of Three, 3?, 150 Rupartus Lincoln~eNis. Scr Greathead

Ss'adia ben Joseph (c. 930)s 193 Sabbionetta. Sec GhcrPrd0 Sachau, E. C., 153, 185 Sacrobmco (c. 1150)~ 1 2 1 Sadasuke. Sec Fujit? Sadlerian profesaomhlP, 466 Sahib al-Qible (c.900)~ 191 Sahl ibn Bishr (c.850)~ 172 Sa'id ibn Ya'qOb (c. 915), I76 Sa'id ibn Yfisuf (c.930), I92 Saintsbury, G., 310 Saint-Vincent, G. de (c. 165o), 424 Salhab ibn 'Abdasalam. Sec &Farad! Sallusti, G. de', 3 m Salmon, G. (c. 1850), 461 Samos, 59, 61, 70 Samuel hen Abbas (c. 1175)~ 109 Sama'il. See Samuel Sand Reckoner, I13 Son-k'ni Chung-ch'a, 151 San-tofit-shu, 143 Sargon (c. 1750 B.C.), 37, 38 Sarkar, B. K., I53 Sarton, G., 498 Sat6 Seikir (c. 1665), 439 Saunderson, N. (C. I730), 454 Saurin, J. (c. 1710). 472 Savasarda (c. IIW), 106 Savile, H. (c. 1 6 m ) ,. 395 Savihn profeuorshrp, 395 SavioU, G., 516 Sawaguchi Karuyuki (C. 1665), 439 S d e s of counting, 9, 41 Scpndinavia, 140, 527 Scardeone, B., 146 Schall von Bell, J. A. (c. 1650), 436 Schanz, 158 Scheubel, I. (c. 1550)~ 329 Scheybl, Scheybel. Sec Scbeubel Schindel (Sczindel), J., 258 Schiegel, G., 18, 13 Schmidt, M,, 14 Schmidt, M. C. P,, 91, 303, 111 Schmidt, W., 115 Sch'dner. See Schoner Schoner, A. (c. r560),335 Schoner, J. (c. 1530)~ 335 Schoncrus. Sec Schoncr ~choolhouse, oldest, 38 Schooten, F. van (c. 16501, 425, 311,

375, 377 Sehmtcn. P. van (c. 1670). 415 Schooten, van, family, 415 Schreiber, H., 348. See also G m -

mateus Schmyber. See Gnmmatcus

DEX

Scbraeder, L. von, 72. 98 Schuere. See Van der Schuere SchulteSs, K., 195 Schultz, A. (c. 1600), 331 Schultz, W., 69 Schur, F., 480 Schurrfleisch, 189 Schwartzerd. See Melanchthor.

Score, 13 Scott, Michael (c. 1225), 220, a 1 0 Scriptor. Sec Grammateus Scultetus. See Schultz, A. Sea Island Arilhmetic Chssic. 1i.2 . . Sebokht (c. 650). 166 - . Secant, I75 Sedillot, L. P. E. Am., 30, 289 S e f n ha-Echnd, 207 Sefer ha-Misbnr, 207 ~ e j e r J L E ~ O , t88 . Seki Kawa (c. 1680), 439, 535 Senkereh, 39 Serenus, Qulntus Sammanicus (c. zoo),

132 Serenus of Antinoopolii (c.so?), 126 Series, general, 48, a66, 271; infinite,

31% 410, 449, 533; logarithmic, 434; trigonometric, 409

Serret, J. A. (c. 1865), g m Sesastris, 51 Seti I (C . 1350 B.c.), 50 Sexagesimal system, 24, 41. See also

Fractions Sextus. See Africanus Sfortunati, G . ( c . 15341, 306, ass Shadib (14th century), 141 Shakesocare auoted. ?n. 106 Shsng ' ~ a o , iI~ Shapiro, H., 174 ShPtir, Ibn al- (c. 1350), 289 She Huang-ti (c. 2 2 0 B.c.), 138 Shiba Tatbu (<<A). xrr .. . Shiiyoshi. See ~ a h Shi Huang-ti, emperor (c.zr3 B.c.),

30, 138 Shirazi, J. K. M,, 286 Shirwood, Bishop, 199 Sh6toku Taijhi (c. boa), 151 Shu-king, 14 Shun, emperor (c. zaso B.c.), 25 Shu-shu-ki-yi, 142 Siber, Rinner and, 299 Sicily, 59, 61 SiddMntas, 145, 156, 157, 167, 168

SiC Fang-tsu (c. 1650), 436 Sieve of Eratosthene, 109 Sixhart. a18 Siiberberg, M,, 207 Siliceo. See Blasius, J. M . Simony J., 375 Simon, M. (c. 18901, s46! 8? Simone. See Francesco dl S~mone Simony, C. de, 232 Simpson, T. (c. 1750), 457 Simson, R. (c. 1750). 456 Sinan ibn TBbit ibn Qorra (c. gqa), Sindhind, 167 Sind ibn 'All. See Abi'l-Taiyih Sine, 156, 175 Siu Yo (c. 1501, 141 Sintus N. a60 Sixty, scale of, 41 Skeat, W. W., 169 Slide rule, 340, 394 Sluse (Slusius). See Sluze Sluze, R. F. W., Baton de (c.1660),

425 Smith, C. F., 313 Smith, D. E., xv, 98, zoo, 107, 332,

3531 409, 462 Smith, H. J. S., 467 Smith, R. (c. 17501, 448 Smith, T., 103 Smith, W., xvi Smogo1cnsl;i (c. 1650), 436 Smvma. ra. 6r myth, c ~ P . , 44 Snell, R. (c. 1600), 422 Snell, W. (C. 1610), 423, 331,343 Snellius. See Snell Snvder. Carl. I07

(c. 425 'B.c.), 79 Sale, F. dal (c. ISSO), 3r3 Solid numbers, 90, 155 Solids. See cube, polyhedrons Solon (c. 600 B.c.), 65 Sonyei. See Araki Sophists, 81 Snroban ..~ - - -~ .,.**; South-po~ntlng vehicle. See Compas Spain, 192, 205,343,434 Spencer, H., quoted. 3 S~eusippus (c. 340 KC.), 90 Sphere, volume of, 156; astronomical,

912 94, 127, 136, 167 Seherics. Sce Smere, astronomical Spirals, 3, 44, 107, 1x4, 136, 387 Sporus of N ~ a a (c. 275), 132 Square, diagonal of, p8 Square root, 155

INDEX 593

Square roots, tables of, 40 Swineshead. See Suiceth Squares, tables of, 40 Switzerland, 348 Sridhara (c. 10201, 274, 280 Syene, 59, 61, 110

Stabili. See Francesco di Simonc Sylow, L., 527 Stiickel, P,. 480, 521, 524, 528 Sylverter, J. J. (c. 18501, 463, 532 Stageira (Stagiral, 59, 61, 93 Symbols, of derivatives, 425; of oper- Staigmiillrr, H., 251 ation, 258, 330, 341, 394; of pro- Stapulensis. See Faber portion, 394; of relation, 320, 389, Stationarius, 244 394; for unknown, 280, 312 stsudt, K. G. C. von (c. 1850), 505 Symonds, I. A., 2441 346 Steele, R., 224 Synesius (c.410), 136 Steichen, M., 343 Syracuse (Siracusa), 59, 61, 113 Stein, M. A., 140 Syriac numerals, 8 Steincr, J. (c. 18401, 524 Syrians. Sec Arameans Steinachneider, M. (c. 185o), 545, 128, SZ* Sian6 (four figures). 15

174. 188, 2 0 7 , 209, 211 SzG-ma T a (554), 151 steilai polygons, 218, 236 Stephen of Alexandria (c. 61o), 191 r (Greek letter) for zero, 204 Stephen Dusan, 242 Ta'Psif (c. 1200i, 287 Sterck van Ringelbergh. See Ringcl- Tabari ( c . 8 4 , 169

bergius Tabit ibn Qorra (c.870), 171, 209 Stevin, S. (c. 1590)~ 34a, 133 r i b i t the Younger ( c . 9401, 1 7 2

Stevinus (Steven,Stephan). SecStevin Tables, 40, 58, 129, 131. 138, 175, 314. Stewart, M. (c. 17501, 456 534. See ofso Chords, Mortality. Stiatteri, A., 545 Multiplication, Rools, Sine, Tan- Stiefel. See Stifcl gent Stifel, M. (c. 1525), 327 Tagliente (c. 1515)~ 304 Stirling, J. (c. 1750). 449 T o 'hhlrlo, 207 Stobzus (c. soo), 92 Taika (ToyotomiHideyoshi) (c. 15901, Stiiffler, J. (c. IS^), 317 352 Stone Age, 15, 21 Tait, P. G. (C. 1880)~ 470 Stanc masonry, 2 2 T'ai-yen calendar, 151 Stow, J., 204 Taiyib (C. 890). 174 Strabo (c. 101, 122 Takabara Kisshu (c. 1600), 437. 353 Strabus, Walafried (c.840), 188 Takebe Hikojirir Kenkir (c. 1722), 535 Strachey, E., 278 Tolckis. See Albanna Strecker, 189 Tallentyre, S. G., 404, 480 Strutt. J. W. See Rayleigh Tamerlane (c. 1400), 287 Suan-king, 19 Ta-nao (c. 2 7 0 0 n.C.1. 24 Suan-pan, 352 Tang Dynasty (618-9071, 149 Substradia, 345 Tangent, 175 Suiceth, Richard (c. 1345)~ 236 T'ang shu, 149

ulsset. See Suiceth 3 ' - T'ang Shun-ki (c. 1550)~ 351

ulvarutros, 97, 98 Tanncry, P., 544. xv, 83, 89, 103, 108, Sumorio Compendioso, 353 125, 128, 132, 133, 136, 207, 234, Sumeria, 35, 37, 39, 146 235, 375: 3771 499 Sundial, 49, 91, 122, 125, 146 Taqi ed-dln (c. 1575)~ 351 Sunon, Master (c. 1340). 240 Tarentum, 59, 61 Sun-tzl (1st century ? i , 141 Tgriq. See Ya'qOb Sun-lai' Suon-king, 141. 152 Tartaglia, Nicalo (c. 1545), 297 Surveying, 43, 52, 81, 124 Tartalea. See Tartaglia Suryadafa (c. 1 ~ 3 5 ) ~ 351 Tares, 45. 46. 47, 49 Stirya Siddhdnta, 34, 145, 167 Taylor. B. (c. 1720). 451 Suter, H. (c.zSgo), 546, 165, 177, 212, Taylor, J., 158

142 Taylor's Theorem, 451, 454 Sven, Master (c. 1340), 240 Teiken. See Fujita

INDEX

Telescope, 365, 409 Ten, s d e of, zo Teniin (c.800). x5i

~ -

Ten&, 53; Terquem, O., 207, 214 Tetrabiblos. See Ptolemy, C. Textbook writers, A I ~ ~ . - Thabit. See Tibit Thales (c . 600 B.c.), 64 Thaaos, 59, or Theetetus (c. 375 B.c.), 86 Thebes, 49 Theodore of Tarsus, 185

Trebizond. See Geoge of Trebizond Trembley, J. (c. I ~ w ) , 525 Trenchant, I. (J.) (c. 15651, 314 Treutlein, P,, 197 Treviso Arithmetic, 148 Triangle, 40, 156, 158; right-angled,

160. 163: Pascal's (see Pascal) Trigonometry, 119, 126, 145, 156, 175,

176, 177, 272, 324, 331 Trigrams ( l ' n -kw) , 25 TriSntika. aia ~risection df'an angle, 118, I71 Trivium, 180

Theodorus tc. I I IO . , a 1 7 Tropfkc. J., xv Theodonu of Cyrenc (c.425 B.C.), 86 Tr'ai Yuan-ting ( r . 1180 . 167 Theodosius of Bithvnia (c. ro B.c.), Ts'al Yune (c . 100). 1 1 1 ~ . -

125 ~schirnhaisen, E. W.,' Graf von (c. Theddosius of Tripoli (c. IW), 125 1690), 417 Theon of Alexandria (c.390)~ 136 Tsu Ch'ung-chih (c. 4 p ) , 143 Theon of Smvrna (c. 121). 120 Tu Chih-chin= (17th centurv). ~ 3 6 ... .- ~heoohrmtus'(c. 3io B.<); 83,'94 Tiimau. D.. 1-88 '

~

~heu'diur (c.360 B.c.), 92 T'u-huo-lo,'r49 Thibaut, G., p8 Tun Ch'iian (c.425), 143 Thibetan "Wheel of Life," 27 Turner, E. R., 166 Thiele. G.. 186 Turrecremata. l.. 1a8 ~hompsod, R. C., Thompson, W. See Kelvin Thomdike, L., 135 Thureau-Dan~ln. F.. 18

... . Tdri (C. IZOO), 188 Tdei's staff, 288 Twelve, xale of, 11 Twentv. d e of. 12

Tb;tmase 1 1 i (c. I & B.c.), so ~ v l o r . ' ~ . B.. 14 . . Thymaridas ( c . j ~ o s . c . ) , 91 Tjrre,'sg, 61 Tibbon, Moses ben (C. IZSO), 209, 210 Tibbon family, 210 uiiain, '54, IS!. Tifernas, Gregory (1458)~ 260 Ulpianus, Domltus (c. am), 131 Timieus, 88 Ulugh Beg (c. 1439, 289 Timur. See Tamerlane Umbra versa, 175 Tittel. C., 121 Unger, F., 256 Todhuntcr, I (c. 1850), 468,382 Unit fraction, 45 To?ndnp, J., 137 United States, 531 Tonml. See Zuanne Units of counting, 7 Tonstail, C. (c. 1522), 316, 314 Units of measure, 7, 38 Topics for Dhcusdon, 19, 53, 101, 147, Unity, 7?, 93

193, 265, 191, 357, 4433 547 Univerntles, 188, 2 1 1 , 231, 245 Torauemada. J., 248 University of Paris, 188, 245 Torfes, T. (i.;swj, 264 Torricelli, E. (c. 1640), 366 Tortolini. B. (c. 1860). 118 - - - ~ - ~ ., - Torus, 1;8 . Toshihisa. See Iwa~aki Trail, W., 456

Ur, 38 Ursinus, B. (c. 1620), 420

Vacca, G., 302 Valla, Georgius (c. 1475)~ 247 Vanin, A. F., 343

Trajan, I46 Vanderbanck, 455 Translators, periods of, 176, am, 103 Vander Hoecke (c. ISIS), 341 Trapezium. SCE Trawzoid Vandermonde. A. T. (c. 1775). 481 Trapezoid, 3a,40, 163- Van der Schuere, J. (c. 1590), 341 Trapeeuntios See George of Trebi- Van Schooten. See Schooten

zond Van s3Gravesande (c. r730), 526

INDEX

Vansteenberghe, E., a58 Vashamihira the Elder (c. zoo), Varaharnihira the Younger (c .

145, 152, 754, 156 Varignon, P. (c. 1700)~ 470 Varro (c. 60 B.c.), 110 Vassilief, $29 Vassura, 366 Vaulezard, J. L. de, 311 Vaux, W. S. W., 164 Vedas, 35, 97 VeUa, P. F. S., 304 Ventuti, P. T., 104 Veratti, B., 178; &a Verbiest, F. (c. 1659), 436 Verga, J. (c. 1450). 263 Verino. U.. a46 victorkus: See Vidorius Victorius of Aquitania (c. 45o), Vicuiia, G. (c. 1880), 546 Vieta, F. (c. 1580), 3'0 Vihte. Sec Vieta Vigesimal scale, 12 Vijagonito. See Bija G a ~ i l a Villani, F., a3a Vincent de Beauvais (c. laso), 226 Vina. Sec Leonardo da

Vitello (c.la)o), a28 Vitruvius (c.20 =.C.), 123, 85 Vittorino da Feltre (c. 1a.30). Viviani, V. (c. 1660); 361 Vizinho, D. M. (c. rgoo), a63 Vogt, H., 75, 91, 98, 105 Voltaire (c. 3745), 477, 404 Volterra, V., 499, $14 Vossius, G. J., a21 Vyutkalita, I62

W=schke, H., a34 Wakkar, Joseph ben (c. 13So), 241 Walafried Strabus (c. 8401, 188 Walcherus (c. IIZO), a05 Wallace, W. (c. xsro), 458 Wallinbv. 0. Sec Levbourn. W

Walsb, J. J., ara Wang Fan (c. 265). I42 Wane Hs'iao-t'une (c. 625). I r o wan; ~ o n g , (c. 41:); 143- Wang Pao-hang (c.554), 151 Wang Pao-san (c. 554), 151 Wang Pi (c. 245). 142 Wappler, E.. a m Ward, A. W., 339

Waring, E. (c. r780), 469 Wasan, 538 Waters, W. G., 247 Wax tablet, 58 Weidner, E. F., 37 Weientrass, K. (c. 1865), 5og Weissbacb, F. H., r o c Weissenborn, H., 178, 195, 283, 417 Werner, J., 331 Werner, K., 184, 195 Wertheim, G., a07 West, A. F., 186 Weyr, E., 4s Whewell, W. (c. 1840), 546, 396, 40% Whish, C. M,, 153 Whiston, W. (c. 17oo), 451 Whitford, E. E., 412 Widman (Widmann), J. (c. 14po),

INDEX

Wu-ts'ao Swan-rhu, 152 Wu Wang, emperor (c. lI2a B.C.1, 11 Wylie, A., 31, 32, 272

Xenocrates (c.350 B.c.), 91 Xylander, G. (c. 1570). 333,133, 343

YBsimln '(c. IZ&), 288 Yau, emperor (c. 1350 w.c.). 14 Yehuda ben Rakufial (c. loth cen-

tury), 208 Ye-lii Ch'u-ts'ai (c. 1130), 271 Ye-lii Hi-liang (c. 12601, 268 Yenri (circle principle), 535, 536, 538 Yi-ching. Sec I-kinr Ying (female principle), 25 Yonge, C. D., 116 Yorizu, 144 Yoshida Shichibei K6ya (c. 1640), 437,

353 Yu, emperor (c. 12w B.c.), 19

Yiian Yiian (c. 18101, 535 Yuen Hao-wen ( c . 126o), 271 Yuen-Shih, 271 YGnis iYGnos).'Alf . . . ibn (c. 1000). . .

17,5, 191 YGnm, M&% ibn (c. ~ z o o l , 287 Yasuf ibn I b r a f m (c.8751, 17a

Zaccagnini, G., 539 Zaddik, Isaac (14th century), 241 Zeitschrift f i r Madathcm~~tik und Physik

(HI. Abt.), 195 Zen0 of Elea (c. 450 w.c.1, 78 Zenodorus (c. 180 B.c.), 118 Zero, 162, 207, 130, 270, 274, 277 Zeuthen, H. G. (c. 1900). 543, W. 153 Ziegler, A., a60 Ziegler, T., 186 Zodiac. 21. .m. IW -. zoroasicr, 71 Zosima (15th century), a62 Zuane. See Zuanne, Giovanni, John,

Joannes, etc. Zuane Mariani. See Madani Zuanne de Tonini da Coi (c .~g)o) ,

295, 3 m Zubler, L. (c. 16071,361 Zudrraga, J. de, 354