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223 Index of Technical Terms

This index contains all terms relating to mathematics, astronomy and technology which occur in the Arabic text of "On Burning Mirrors", arranged alphabetically by roots. All occurrences are listed, except that for those terms occurring a large number of times only a repre­ sentative selection of instances is given, followed by "al. " (other occurrences), "fr." (occurs frequently), or "passim". References are to sections. If a term occurs two, three or more times in a section, this is indicated by a raised "2", "3", etc. following the relevant section number. If a section number is enclosed in angled brackets, that means that the term appears in that section through my restoration or emendation. If a section number is starred, that means that the commentary on that section discusses the term. The forms of the verb are indicated by the conventional Roman numerals. Nouns are characterized as such by the addition of the article "al-" (except where it would be awkward for some reason, e. g. for nouns in the construct case), whether or not they have the article in the passages referred to.

224 y - \

\

..;'1\ 172

U\.,,1-'1\ 136, <149), 243 3 vl-'1\ 21, 33

./''1\ v. ~p\

U)r\ 25, 36; v. -.:.J~U\

:,;\ 57, 68, 185, 206, 245

-.\~\ 51,54, <91)

U~ \')\ 166

J.)~ 45,71,74

(.;)~pJ\ 7, 186,242,243

~ <130)

~\ 3,4,82,92, 10,29,51,52,62, al.

~\ 125

~\ 9,62,97,98, 101, 102, 115, 126, 193, al.

~\ 77

42,240,241

225 Index of Technical Terms

~~ II 5, 7, IS, 16, 22, 23, 27, 145, 148, 149, 245, al.

~~ V 48, 76, 111, 140, 141, 143, 204, 218, 221, 226, 234, 239, 244

~ 67, 128, 135, 154, 190, 207, 210, 220, 229

cA. IV 51,54,91, 110 ~\,. 16 ~I 44, 83, 231, 232, 236

.)1 1752, 183

~ 53,57,70,982,99, fro

c:-- VIII 3, 4, 6, 13, 118 y~ c:r FI 120, 121, 1222, 156, al.

t~ 139, 1562, 1574, aI.

~ 9, 34, 43, 502, 55, 59, 61, 74, 128, aI.

~_~ 137,144,1552

;;4- IV 45, 113, 131, 163, <163), 237, <238)

~;I <243)

226 t-y

CI.1> IV 17,47, 50, 56, 59, 67,76, 81, 109

CI.)~ 55,95

~))I 11,95

J r IV 4, 16, 17,342,36

J~ 36; v. ~\';I

Jlr'il 122,32,333,34,35,59,95,97,111

.:)r V 110

1.~ IV 8, 91, 129

~ .JI~ ~.l..>- 3,32, 55, 197, cf. 562,57, 59, 60, al.

J\ll 502,61, <1092)

(.f" IV 9, 392,40, 41, 482, fro r/" X 139

(..J\> 40, 89·, 161

1. J~I 136, 140, <140), 1422, 143 iu_J1}1 ~\.Q)I 1. J~I ~ 8·, 15,32,38, 103, 108, cf. 10, 124,207

-.l..> 208, 222, 235, 236

-.l..> II 110, 219

1JI 384,394,502, passim; v. ~, ~, ~

227 Index of technical te~s

j.> 24

).> IV 8, 15,51, 54, 56, 61,91, 101, 193, al.

; .;1..01 57, 602, 622, 101, 102, al.; v. ~

~I ;.;1..01 94

; .J I.> '11 15, 92

~1.JJ..01 56,61,66

.J

V"\ )1 137, 233

I,$\.J (= subtend) 125·, 128, 133 2, <133), 1345

;:T)Iu 3,4,14,17,31,34,97

2,8, 16,31,96, <97), 252

216·

864, 99, 105, 112, 114, 1182, 156, al.

91

60, 62, 126, 194, 195, 196, 197, 198, 223

r-)I 28

228 '-'" - .)

t~.J '1\ 1372, 1422, 143

~.J II <232> ~~\ 174·

~)\ 12,56,57,68,78, 101, a1.

18, 22, cr. 23

i::.~)\ 36 J\) '1 240

~-J\)\ 444,456, passim; v. J.. Jf-l\, ~\i

.)\) 102, 11

~.)~)\ 10, 11

JJ\) c:W 171·, 172

JL 3,4, <5>,5,15

~\ 6, 72, 15, 146, 149

~ -,,_~lI...... J\ 202•

~\ 34, 51 2, 53 3, 553, 592, al.

u";---~ L 1\ 98, 109 • , 195, 198, 219

.l...i- IV 42, 121, 201

229 Index of technical terms

~I 9", 140, <140)

~UI 16, 17, <24)

Q~UI Q'1\ 21", <24), 26, 28

JL- 39,40,413, passim ~ JL..::.... 44, 47, 49, 50, 76, 81, al. ~

~ 55

~ 67

~L:..:... 83

.::J~ 42, 121,201,233

c.\...... :.)I 6, 92, 95, cf. 90

Q~\...... :.)I 3,4,9, 11, 12, 13, 14, 17, 51, 52, al.

$..:JI (= figure) 8, 17,91, 110, 129, 232

$..:JI (= proposition) 111,114

;;.;.)\....1.1 18

~I 129, 130

~I 51",55,92 ~UI 32

230 ;.;.,..-ll 232, 235

.;\.- 122, 62, 99, 115, 149, ISO, 161, 162, 181, a1.

.;\.- II 98, 182

y..rJI (- kind) 15 y.rJI (= mUltiplication) 118, 120, 121, 1222, al.

J.,...;.. III 35

98, 182, 186, 199, 2413 v. )r--... JL.. IV <147), 150

yl.l. 6, 187

Y ~ 17, 185, 206, 225, 229, 239, 241

J..,.11 72,733,116,1282,1312,1352,149,240

~• I 1. 'I 21 ,4,282

231 Index of teahniaal te~s

~ 109, 129, 195, 198, 219

~ VII 3, 4, 9, 112, 13, 142, 17,47,49, 522, aI.

J\J.....jY\ 12, 17,50,63,772,90

~\ 52,743,75, 125, 135

~ v.o)\..0\

~ <27),30,33,40,58,174

~ V 27

~ V • II 100, 1092, 112, 130, 176, 180, 191, al.

~\ r}J\ 19

~7

r}-.. 10,97,98, 141, 144, 1472, 148, al.

.;.u)\ r}- 146 c::- ~\ r}- 1462, 1502, 164, 1702, 1722

.)~\ 39, 62, 104, 1373, 164, 173, 1922, al.; v. c.,$ ~

~ 6·,7, 15,25,282,29,31,36,51,92, al.

J..-l\ 6, 16,25,26, <27), 29, 110,2422,243

J~ 32

.)~ 51,54, <61)

~ 16

~~~ 57, 182, 185

232 J-t

~ 53, <69), 209, 215, 216

~ II 144,184

J.-Al\ 352

~ 113,114

J~ 116

.;J.il\ 125, 128; v . r.,Lu .; \o1il.\ 34, 57, 65" r J.il\ 34" ,.::.A... J.al\ 5

y,} 125 y~\ 94 y,}\ 773,902,94,95

y)id\ 219

y.;\:A::.... <191) I,;)J~\ 109" r....i 127, 147, 150

~.r-i 39, 43, 44, 76, 78, 802, al.

8",38, cr. 39

233 Index of technical te~8

L...-iJ\ 150

.rd\ 72,240

~\ <31),342, 105, 112, 1382, 140,208, al.

..,..1i J.-.i 20, 137,222

~ 59, 88, 89, 90, 101, 102, 110, al.

~ VI 188,198

~\ (= section) 39,48, <53), 56, 61, 64, 207, al.; v. .1.. J~\'

Jj\). ~\;

~\ (= cutting) 193, 194

~\ 13,612, 66,96, 1362, 1372, 234, al.

do\i 79, 214, 222

;~\.Q)\ 44, 1362, 137, 140, <140), 1422, 143,233

~\ 129

~\ 97,110

r 51 2,55

~ 16

~\ 17

y3\.Q)\ 110·

V" ~\ 79, 802, 81, 882, 89, 91, 135,2092, 215 2, a1.

18,22

53,60

J; 103, 105, 176, <177), <191)

~ -k 12,125

234 J -J

~\g 462, 53 2, 55, 602, 61, 83, 98, 116, 152, 232, 235

~~J\)\ ~\g 44, 232; v. J., J~\

U\g ~\J) J; 40,41, 53, 57, 602, 61, 64, 235, al.

~~ '1\ ~ 45 fAJ 'o?.:J\ U\ 9", 38, 124

~~\ 11, 122, 322, <33), 35 'o?~ 35 45~\ 12

V"'\g 32

V'" UJ\~ 23", 33

V'" L.il.\~ 16, <23), 24, 28

~ p\ 122, 13 2, 142, 20, 91, 96, 1362, 1372, al.

~\ 1862, 1872, 1992, 2062, 221 2, 2262, al.

I;)IS' ~ 76, 127

J

y)'1 66'

~ <40),47, 51, 68, 88, 89

I;) ~~ '1 I;) \.:ill \ I;) \iJ \ 171'

~ VIII 100, 233

~\ 98,110

235 Index of technical te~s

r

9, 62, 862, 102, 107, al.

(. e. g.) 48, 221

34, 873, 122, 123, 177, 178, aI., cr. 175

187, 190, 2062

102, 138

49, 51, 59, 602, 65, 67, 171, al.

35, 862, 118, 120, 121, 122, 175, 178, a1. v- III 39

~W.\ 48

~\... 662

~\...... <47),48,49,50

~ pi; 116

~ 243

~~... r\ 4,18,82

~U\ 89,242

~\ 132S, 1372, 1393, 1573,2062, fr.; v. J\~

~l.... 245 2

J.-J\ 13, 143,38,59, <59), 169, 189,232; v . ..,--i. ).aA1\

~ II <241)

236 J - r

~ 148, 197, 242

170·, 172

~ VIII 224

186

J

~J 3,4,36, 1752, 178, 208, 245, al.

~\ 100, 130, 195·, <208)

)y 45,48, 67, 68, 77, 80, 88, 163, al. ~ )\~ 50, 52, 76 + t'L:.. '1\ 'r?)\~ 154 J...... )\ 97·

.la..::..~ 208

...... ;...,. J 98, 146, 180, 223, 224, 235

J-J 41,48,53, 69, 80,98, 117, 2173, al.

237 Index of technicaL terms

e::. J 126, 188, <197), 235, 236, 245, at.

c:-)\ 66;v. r~ c:-).\ 13*, 14, 16, 17,34, 51, 54,91, at. t.ry 53, 66, 78, 125

~J 59, 81, 82, 94, 95, 105, 116, at.

~J l. J.$' 39, 176, 180

e..,t)\ 94 JJ VI 2442 J\p 215 -~ ~ J\p 205·, <210), 21'3, 2182, 220, 2262, 246, 248, 2511

238 General Index

This index contains all mentions of all proper names in the book (excluding the preface), with the following omissions: purely biblio­ graphical references, trivial occurrences of II Diocles" , and names of cities where manuscripts are located. It also constitutes a selective subj ect index. References preceded· by § are to section numbers of the text of liOn Burning Mirrors". All other references are to page numbers.

Abu Bisr b. Sahl, 30 Ambrosian Library. Milan. 19 Abu )l-Badr cAbd al-'Azlz: Ammonius: son of Hermias, addressed by ibn Ki~na. 30 probably acquaintance of Abu )l-FutuQ.: mathematical Eutocius. 18 n. 2 treatise by. 28; work on Amphipolis: name Pythion at. 138 II Almagest" star cataloque analysis: geometrical. 170. 177 by, 28; work on al-Farabl's : and invention of commentary on "Almagest" sundial, 147 by. 29 Anaximenes:and invention of Abu )1-Wafa : on constructing sundial. 147 with given focal : denoted by single letters. distance. 23; algebraic work 151 by. 29; addresses Abu Bi~r - "mixed": in Bobbio Mathemati­ b. Sahl, 30; ? connected with cal Fragment. 20-21, 157; Mu'ayyid al-dawla Abu in Diocles and elsewhere. Man/?ur, 30 . 156-7 Akbar, emperor: used l1iihi Era, Anthemius of Tralles: used form 26 n.4 ltupl;ov 3 n. 1; focus of Akf8:nI, al-: mentions Diocles' parabola in, 15; character~ treatise. 16. 21 istics of his treatise. 16 n. Alexandria: ?Eutocius at. 18. n. 20. 20. 22; on history of 18 n. 2; school at in late burning mirror. 16; used antiquity, 18. 21; distance focus directrix property to of. from Rhodes. 147 construct parabola. 17.

239 General Index

17 n. 22, 22; did not know by Archimedes, 13-14 Diocles' work, 18; not author Arcadia: Diocles lived in, 2, 140; of Bobbio Mathematical not a "cultural center", 2; Fragment, 19-20 mentioned, § 4 - Arabic translation of: cU!'arid's Archimedes: conics in, 4, 5, 6, "revision" of, 20; referred 14-15, 150, 166, 168; main to by ibn al-Haytham, 22, source for pre-Apollonian 22 n. 22; mentioned, 20, conics, 4, 4 n. 2, 5; names 21 n. 16 of conic sections in, 4, Apollo, pythian: principal deity 4 n. 3; Syracusan dialect at Thasos, 138; and doubling used by, 4 n. 3; references of cube, 169 to "elements of conics" by, Apollonius of Perge: date of, 1, 5, 5 n.4, 150; terminology 2 n. 8, 10 n. 1; work "On the of, 4, 5, 6, 13, 15, 141-2, Burning Mirror" falsely 163, 165, 167; symptomata ascribed to, 16, 20, 143; of conics in, 6; burning "Thngencies" of, 16, 16 n. 19; mirror allegedly construc­ ?knew Diocles' work, 16, ted by, 22, 22 n. 22, 28; 18 n. 1 editio princeps of, 23; - "Conics" ( 1tWVI." 1t eX) : studied by alleged references to by of 16th and 17th centuries, Dioc1es, 1, 170, 187, 189, 24; mentioned by Diocles, 1, 191; innovations in conic § 136, § 149, 179, 181; friend theory in, 7-9, 14, 15 n. 12; and correspondent of Conon, terminology in, 7, 14, 152, 139; correspondent of 167-68; publication of, Dositheus, 140; took parallax 10 n. 1; foci in, 15, 15 n. 13; into account, 145; distances focus of parabola not between heavenly bodies mentioned in, 15, 170; omits according to, 146; omits theorem that subnormal of steps in proofs, 156; used parabola is constant, 22, inequality to solve triangles, 151; Arabic translation of, 158, 162; bounds for 13 given 33, 138-9, 139, 142, 152, by, 158; assumes that two 167,168,170; construction mean proportionals can be of in, 167. See also found, 169; his "Axiom", conics, theory of; parameter 174. See also application of application of areas: as method areas; conjugation, oblique; of formulating second­ conjugation, orthogonal; degree equations, 7, 7 n. 12; Eutocius; parameter used by Apollonius to define - problem left incomplete by: symptomata of conics, 7; solved by Dioc1es, 1, 2, 162, ?used in conics before 164, 179-93; solved by Apollonius, 13-14; ?used Dionysodorus, 2, 2 n. 9, 164;

240 General Index

solved by ?himself, 164,168 Balabish: horn? strigils found at, 160 - "Sphere and Cylinder": II 1, Barocius (Barozzi), Franciscus: 169; II2, 163, 205; II4, 163, first in west to use name 164, 206; II 5, 171; mentioned II cissoid" , 25 n.40 by Diocles, § 136, § 149, 179, Beeman, W.O., 27 181 Belger, C., 19 n.8 Aristaeus: treatise on conics by, Berenike. See 5; alleged discovery of focus­ BfrunT, al-: epitome of his work directrix property by, 17 on specific gravities, 30 : distance Bobbio: monastery of St. from earth to moon accor­ Columban at, 19 ding to, 146; used inequal­ Bobbio Mathematical Fragment: ities to solve triangles, uses form nup 'Co \I, 3 n. 1; 158, 162 focus of parabola in, 15, 21, Aristotle: Elias' commentary on 202-3; mentions Apollonius' "Prior Analytics" of, 18 n. 2; "On the Burning Mirror", uses single letters to denote 16, 20. 142-3; knew Diocles' angles, 151; "mixed" angles work, 16,20,143; palimpsest in, 157; "leaden rule" in, 160. containing, 19; editions and See also Simplicius studies of, 19 n. 6; Artemis Brauronia, 153 facsimiles of, 19 n. 7; author­ Asclepius, 153 ship of, 19-20; character­ "astronomers, the", § 18, § 28, istics of, 20; date of, 20; 145 archaisms in, 20-21, 157; astronomy: nature of, in Diocles' spherical burning mirror in, time, 145; early Hellenistic, 155; mentioned, 143, 151 146 Boeotia: name Pythion in, 138 Athena Poliouchos: important brass: in Diocles (?), §51, §55, deity at Thasos, 138 § 92; use of, in antiquity, Athenaeus of Attaleia, 139 152-3. See also OpdxaA){O~ Athens: school at in late anti­ quity, 21; name Pythion at, Brockelmann. C., 29, 30 138. §ee also Lamptrai, bronze: ancient mirrors made Zenodorus from, 152; Arabic terms for, Attaleia. See Athenaeus 152 Aurangzeb, emperor: library of, 26 burning-glass: in antiquity, 149; Autolycus: on "spherics", 145; (?)in Diocles' text, 149 term &aVl11tTWTO~ in, 168 burning mirror: Greek name axis: of conoid, 9, 142; Arabic for, 3, 3 n.1; Arabic works term for, 142 on, 21. 21 n. 17. See also - of conic: meaning, 6; in Diocles, Apollonius; Archimedes; 9, §8, §38, §39, 141 Diocles; Dositheus; nup'Co\l

241 Genel'al Index

- parabolic: 3. §8. §32. §51. §55. - early history of: 3-6.10-15.17, § 97. § 111; invented by 168; in light of Diocles' work, Dositheus. 16; work by ibn 4. 9 al-Haytham on. 22. 203-4; conjugation. oblique: defined. used as sundial. § 16 - § 17. 8-9; in Apollonius. 8-9; 143. 148. 154 in Diocles, 9. 15. 167; in - spherical: 3. 20. § 12. § 32. Archimedes. 15. 167 §§ 91-92. § 96. 142. 143. 155. conjugation. orthogonal: defined. 156 6; characteristic of earlier conics. 6. 13; in Diocles. 9; in Archimedes. 167 Callimachus: mentions bpe;CxaAXO!;, Conon: mentioned by Diocles. 153 2, § 3; acquainted with Cantor. Moritz: errors of. pythion. § 3. 139; date and 1 n. 5. 15 n. 14. 19 biography of. 139; death of. Casiri. M •• 23 mentioned by Archimedes. chord: no term for in Greek. 154; 139. 140; friend of Dositheus. mentioned. § 53 140; interested in conics. 140 cissoid: used to determine Cos: "town of Archimedes". 28; Diocles' date. 1; used to name pythion at. 138 double the cube. 3. 23. 172; cube. doubling of: solutions by origin of name, 24-5; Diocles of, 3, 169-70. 171. etymology of. 24; mentioned 172. 173; early solutions in antiquity. 24-5; identi- of. 23. 24. 169; solution fication of. 24, 24 n.36; by al-Khazin of. 23; name not used by Diocles history of problem of. 169; or Eutocius. 24. 172; equivalent to finding two Diocles' not called mean proportionals. 169 xl.crcroe;l.on!;, 24; origin of cubit: as unit of measure in modern identification of Hellenistic times. § 31. unknown, 25; mentions of. in 148 17th century, 25 Colophon: name IYthion at. 138 Coma Berenices: constellation 0: transcribed..9.. in Arabic. 138 of. named by Conon. 139 Delhi. See Nadir Shah Commandino. F.: did not identify Delian problem. 169. See also "cissoid", 25 cube. doubling of conics. theory of: place of Descartes, R.: recipient of Diocles in, 2, 9-17; in Fermat's II Methodus" • Apollonius. 7-9. 14-15; in 25 n.38; uses name "cissoid". "On Burning Mirrors". 9-17. 25 166-68; used in doubling the diameter: of conics. 6; meaning cube. 169 of. in Archimedes. 6. 141

242 General Index

Didymus: pseudonymous treatise Dionysodorus: contemporary of by, on burning mirror, 28; Diocles, 2; life and works metrological treatise by, of, 2, 2 n.9; solution of 28 n.10 Archimedes' problem by, Diocles: life of, 1-2; solution 2, 2 n. 9, 164, 168; conical of a problem of Archimedes sundial invented by, 148 by, 1, 162, 164, 205, 209-12; : Arabic translation references to other mathe­ of, 171 maticians by, 2; date of, 2; directrix. See focus erroneous dating of, 1 n. 5, distances: of sun, 144; of moon, 18 n. 4; lived in Arcadia, 2; 145 contributions to theory of - between heavenly spheres: conics, 3, 16, 17; relation­ § 20, 146; measured in ship to Apollonius, 9, 16, 18 stades, 146 n. 1, 20, 167, 168; not author Dositheus: mentioned by Diocles, of Bobbio Mathematical 2, § 6; invented parabolic Fragment, 19 burning mirror, 16, 140; - work of: title of, 3; contents life and works of, 140 of, 3; alters received notions of history of conics, 4, 10; terminology in, 9 Eaton, Ethel: on meaning of 10, 167, 168; archaisms in, OPELXQA}(O!;, 153 9, 21, 22, 151, 156, 156-7; "elements of conics": mentioned translation of, into Arabic, by Archimedes, 5, 150; 21, 22, 29; name "cissoid" meaning of, 5; theorems in, not used in, 24, 172; inter­ 5, 6, 9, 150, 150-51 polations in, 31, 149, 154, 155, 161-2, 165, 168, 173; Elias: Eutocius mentioned by, steps omitted in proofs in, 18 n.2 156, 157; use of inequalities Elis: name Pythion at, 138 in, 158; use of "Archimedes' ellipse: generation of, in early Axiom" in, 174. See also Greek conics, 4, 10-11; ellipse; Eutocius; focus; Apollonius' generation of, 7; ; parabola symptoma of, 5, 6, 11-12, - influence of: in antiquity, 15; parameter of, 7; oblique 18-21; in the middle ages, conjugation of, 167; con­ 21-23; in the 17th century, struction of, by Apollonius, 23-24 167 - name of: original, 4; - manuscripts of: in Meshhed, "Apollonian", 7, 14-15, 167; 26-30, 31; in Dublin, 30-31 in Diocles, 9, 167; alter­ Diodorus Fasparos: decrees in native, 14 n. 10 honor of, 147 : sundial in, 147

243 General Index

Euclid: treatise on conics by, 5; FarabI, al-: Abu )l-Wafa"s work "Optics" by, 161; "Surface on geometrical construc­ Loci" by, 17; "" tions attributed to, 23 n. 29; ascribed to, 143, 151, 155, commentary on "Almagest" 157; on "spherics", 145; by, 29 defines, but does not use, FarganT, al-: on arrangement of "mixed" angles, 157 heavenly spheres, 29; - "Elements": 5, 151; I 43, 167; work(s) on by, 29 I 44, 173; II 8 used by Fermat, Pierre de: letter to, Diocles, 22, 164; II 8 used from Roberval, 25; uses by ibn al-Haytham, 22, 203; name "cissoid" for Diocles' III Def. 7, 157; III 7, 156 curve, 25; possible origi­ (ter); III 31, 151; VI 9, 168; nator of nomenclature, 25 X 1, 174; Arabic work on focus: of conics in Apollonius, last proposition of XV, 28. 15; name coined by Kepler, See also Proclus 15 n. 13; no name for in Eudemus of Pergamum, 139 ancient and medieval works, Eudoxus: axiom used by, to solve 15 n. 13 integration problems, 174 - of parabola: known to Eutocius: excerpts from Diocles Dositheus, 16, 140; not by, 1, 18, 23, 163 (bis), 164, mentioned, deliberately, by 166, 170, 172, 177-201; Apollonius, 16; in late Greek gives title of Diocles' work, works, 16, 21, 202-3; in 3; additions and changes by, Diocles, 16, 140; in ibn in excerpts from Diocles, al-Haytham, 203-4 1, 18, 163 (bis), 164, 170, - -directrix construction of 172, 177; on early history parabola: in Diocles, 16, of conics, 4, 14 n.8; errors 159, 160, 161, 170, 171, of, 14 n. 8, 189; biographical 177; in Anthemius, 17, on, 18 n. 2; friend of 17 n. 22 Anthemius, 18; source of - -directrix construction of all some references to Diocles three conics: in Pappus, 17; in Islamic works, 23; allegedly discovered by source of all knowledge of Euclid, 17; a Hellenistic Diocles in western Europe, discovery, 17 23-24; did not use name foot: as unit of measure in "cissoid", 24 Hellenistic times, § 34, 148 - commentary on Archimedes Fraser, P. : 2 n. 8, 2 n. 10 by: 18, 18 n. 2, 164, 169, 170; Galen: Arabic translations of Arabic translation of, 23; works of, 139, 147, 171 editio princeps of, 23, 25; Gandz, Solomon, 32 error in text of, 163. See : date of, 1 n.5; also cube, doubling of mentioned, 1, 24

244 General Index glass: used to make "burning­ Hippolytus: "Refutation of all instrument". § 36. 149; Heresies" ascribed to. 20 used in ancient lamps. 149; horn: used in ancient artifacts. used in ancient mirrors. 160 149. See also burning-glass Huxley, G" 15 n. 16, 20 n. 10 : of sundial. § 16. § 24. Huygens, C.: discovered proper­ § 28. 143. 144; terms for in ties of cissoid. 24; used Arabic. 145; in Eratosthenes. name "cissoid", 25 147; attributed to Anaxi­ hyperbola: generation of, in mander. 147; replaced by early Greek conics, 4, 10-11; hole. 147. See also sundial Apollonius' generation of, 7; God. § 1. § 252 symptoma of, 5, 6, 11-12; GolchTn-Ma'anT. A1].mad: des­ parameter of, 7, 13 cription of Diocles ms. by. - name of: original. 4; 26. 27 n. 7; on Nadir Shah's "Apollonian", 7. 14-5. 16-7; gifts to Shrine Library, in Diocles. 9, 167 27 n.8 - asymptotes of: work on, by Gomes Teixeira, F .• 24 al-SijzI. 30; terms for, 167-8

Heath. T. L.: erroneous dating of Diocles by, 1, 1 n.5; lasos: name Pythion at, 138 inferred that Diocles des­ Ibn AbI U?aybi'a. 27. 29 cribed parabolic burning Ibn al-Haytham: "On the Para­ mirror. 16 n. 21; noted error bolic Burning Mirror", of Eutocius. 189 n. 1; men­ 22. 151, 161, 168,203-4; tioned. 157.161.170 style of, 22; knew Diocles' Heiberg. J. L •• 4 n. 3. 13, 19, treatise, 22; "On the 19 n. 8. 23. 150. 177 Spherical Burning Mirror", Herakleides: common name at 22 n. 24 Thasos, 138 Ibn Ki~na: work by, refuting Herakles: important deity at al-KarajI, 28; meaning of Thasos. 138 name of, 29 n. 12; work on Hermias. See Ammonius asymptotes by, 30; date of, Heron: solution of doubling the 30 cube by, 23; "miracle­ Ibn al-QiffL 29 working" devices in, 149; "Mechanics" by, 152 Ibn Sina: on arrangement of heavenly spheres, 29; Hipparchus: took account of parallax, 145; determination had al-JuzjanT as pupil, 29 of moon's distance by, 145 llahI Era, 26, 26 n. 4 : and problem inscriptions, Greek, 2 n. 7, 3 n. 1, of . 169 138,147,148. 149, 153

245 General Index interpolations. See Diocles, 2 n. 10; mentioned, 153. work of; Eutocius See also conics, theory of; Isidore of Seville: Etymologies, trigonometry codex of, 19 Megalepolis, 2 Megara, name Pythion at, 138 Menaechmus: theory of conics JuzjanT, al-: work by, on invented by, 4; Diocles' arrangement of heavenly method of doubling the cube spheres, 29; date of, 29 misattributed to, 18 n.4, 169, 193; method of doubling the cube by, 23, 169; knew KarajI, al-: work by, "al-Kafli', asymptotic property of 28 hyperbola, 168 Kepler, J.: coined name of focus, Meshhed, Faq.iliyya Madrasa: 15 n. 13 mss. in library of, 27, Khazin, al-: reference to Diocles 27 n. 8; mss. of transferred by, derived from Eutocius, to Shrine Library, 27,27n. 7 23; work on doubling the - Shrine Library: mss. in, 26, cube, 23 n. 27 27; benefactions to, by KindT, al-: work "On Rays" by, Nadir Shah, 27 n.8 used Anthemius, 20, 20 n.12 mirrors: glass, in antiquity, 149; ?brass, §51, §55, §92, 152-3; bronze, 152. See also lamps: used in temples, § 36, burning mirror 149; made of glass in Molther, Johann: attributed antiquity, 149; character­ Diocles' method of doubling istic of Christian churches, the cube to Menaechmus, 149 169-70 Lamptrai: Athenian deme, 139 Montucla, J. S.: attributed Lebadea: building inscription Diocles' method of doubling from, 148 the cube to Menaechmus, 170 Lesbian method of building, 160 Mu)ayyid al-dawla Abu Man~ur: Letronne, A.-J., 138 Buwayhid ruler of If?fahan, Loria, G., 24, 24 n. 36 ?patron of Abu 'l-Wafa', 30 Mughal Emperors: library of, 26; defeat of, by Nadir Shah, Magnesia on the Maeander: 27 name Pythion at, 138 Mul}.ammad, § 252 Mai, Angelo: use of chemicals Mytilene: name Pythion at, 138 by, on palimpsests, 19, 19 n. 8 mathematics, ancient: conditions under which pursued, 2,

246 General Index

Nadir Shah: brought booty to Diocles, 9, §8, § 1Q, § 15, Iran from Delhi, 27, 27 n.8; § 32, § 38, § 103, § 108, § 124, benefector of Shrine Library, § 207, 141; in Bobbio Mathe­ Meshhed, 27 n. 8 matical Fragment, 20 names, Greek: connection of, paraboloid, 142, 143, 153, 154, with local deities, 138 214-16 Neugebauer, 0., 205, 213 parallax: neglected in ancient Newton, Isaac: discovered sundial theory and astro­ properties of cissoid, 24; nomy, 144, 145, 148. used name "cissoid", 25 See also sun of Gerasa: Arabic parallelogram: meaning translation of, 171 " rectangle" in Greek texts, 165 parameter, name of: in Archi­ Olympiodorus, 18 n. 2 medes, 6, 9, 13, 150; in OPE:LXCXA}(O!;; : meaning of, 152-3 Apollonius, 7, 7 n. 13, 13, 141; in Diocles, 9, § 9, § 38, § 124, 141, 150 (bis); hypo­ Pappus ("Collection"): references thetical, in pre-Apollonian to earlier works on conics conics, 13. See also parabola in, 4; on naming of conic Parion: name Pythion at, 138 sections, 14, 14 n.8; un­ Patara: name Pythion at, 138 reliability of, 14; on focus­ directrix property of conic Pergamum: inscription of, sections, 17; does not mentioning sundial, 147. mention Diocles, 18; See also Eudemus references to "cissoid" in, : method of doubling 24, 24 n. 31; preserves work the cube by, 23 of Zenodorus, 139; "para­ Philonides: acquainted with meter" in, 141 Apollonius, Dionysodorus parabola: generation of, in and Zenodorus, 2, 2 n.8, 139 early Greek conics, 4, 5, Plato: OPE:LXCXA}(O!;; mentioned by, 10; Apollonius l generation 153 of, 7; symptoma of, 6, 7, 17, Pliny (the elder): on invention of 161; parameter of, 6, 13, sundial, 147; on glass 13 n. 5; parameter of, in mirrors, 149 Diocles, 9, § 9, § 38, § 124, R>lybius, 2 141, 150 (bis); focus of, Proclus: on name for ellipse, 15-17, § 9, 153, 202-4; sub­ 14 n. 10; references to normal of, a constant, " cissoid" by, 24, 24 nn.32- 150-1. See also axis; focus 34; on neglect of solar - name of: original, 4, 141; parallax, 145; mentioned, "Apollonian", 7-14; in 18 n. 2

247 General Index

- commentary on Euclid I: editio §198. §219. 159-60. 172 princeps of. 25; Barocius' Sahl b. Bi~r. 30 Latin translation of. 25 n. 40 Samothrace: name Pythion at, proportionals. mean. See cube. 138 doubling of Schmidt, Max C. P.: attributed Ptolemy: "Analemma" of. 19. Diocles' method of doubling 19 n.5; Arabic translation the cube to Menaechmus, 170 of "Planetary Hypotheses" section of an acute-angled cone. of. 29. 146 See ellipse - "AIm age st": al-FarabI' s section of an obtuse-angled cone. commentary on. 29; size of See hyperbola earth in. 144; parallax in. 145 section of a right-angled cone. Ptolemy III Euergetes, 139 See parabola n:up'Cov: name for burning sections, conic. See conics; mirror, 3; spelling of. 3 n.1 ellipse; hyperbola; parabola pythion: temple of Apollo at Sesiano, Jacques. 3 Thasos, 138 Sezgin. F •• 30 (bis) Pythion of Thasos: mentioned Shah Jahiin. emperor: library by Diocles, 2, § 3, § 5, § 15; of. 26; IlahT Era used by. problem posed by. § 3, § 5, 26 n.4 § 15, 143; name character­ Side: name Pythion at. 138 istic of Thasos, 138; Sijzl. al-: work on asymptotes aquainted with Conon, § 3, of hyperbola by. 30; ?ibn 139; date of, 139 Kisna his contemporary. 30 Simplicius: commentary on Aristotle's "Physics" by, Qusta b. Luqa: as translator. 21; 156 work of. on burning mirrors. stades: celestial distances 21, 27; work of, on optics. measured in, § 20, 146; 27; list of his works by ibn Arabic transliterations of, AbI U~aybica. 27 146 Strabo: sundial mentioned by. 147 sun: distance of. in early Helle­ Ramee. Pierre de la: did not nistic period. 145 identify" cissoid", 25 - parallax of: considered Rhodes: name Pythion at, 138; negligible by Diocles, §§ 22- distance of. from Alexandria, 23. 145; neglected in sundial 147 theory. 144; taken into Robert, L., 138, 147. 149 account by Archimedes and Roberval, G. P. de: discovered Hipparchus. 145. See also properties of cissoid. 24; parallax used name "cissoid", 25 sundial: made from burning ruler, flexible, § 109. § 195. mirror. §§ 16-17. 143-4.

248 General Index

148; with and without Thessalonike: name Pythion at, gnomon, § 24, 147-8; shadow­ 138 receiving surfaces of, § 29, translations from Greek into 148; impossibility of Arabic: types of work trans­ burning-mirror sundial, 144; lated, 21; aberrant termino­ terms for in Greek and logy in, 21 n. 16; reversal of Arabic, 147; in inscriptions, figures in, 32; lettering of 147; "roofed spherical", 147; figures in, 32-3; trans­ conical, 148. See also literations in, 138, 139, 146; gnomon calques in, 141; mistakes in, Suter, H., 29, 30 143, 146, 160; technical symptoma: meaning of, 5; used terms in, 147 (bis), 152, 154, to characterize conic 168, 170-1, 171, 172 sections, 5, 6, 7, 13; in trigonometry: not developed in oblique conjugation, 9, 15. Diocles' time, 158 See also application of areas; conjugation synthesis: geometrical, 168, 170, CUHirid. b. Muhammad:. "revision" 177 of Anthemius' work by, 20, 21 n. 16

Tiibit b. Qurra: work by, on area of parabola, 29; on arrange­ Valla, Giorgio: manuscript of ment of heavenly spheres, Archimedes owned by, 177 29 Vitruvius: on sundials, 148 Thnnery, Paul: on identification of "cissoid", 24 n. 36; mentioned, 1, 18 n. 2 Wiedemann, E., 21 n.17, 21 n.19, temples: "miracle-working" 21 n. 20, 29 devices in, § 36, 149 William of Moerbeke: translation Thasos: Pythion geometer from, of Ptolemy's" Analemma" by, § 3; Pythion common name at, 19; translation of Archimedes 138; Pythian Apollo principal and Eutocius by, 177 deity at, 138; Herakleides common name at, 138; Herakles and Athena Zenodorus: acquainted with Poliouchos at, 138; Arabic Diocles, 2, §4, §5; date of, rendering of name of, 138-9 2, 2 n. 7, 139; biography of, Themistius: "De Anima", Arabic 139; ? an Athenian, 139; name translation of, 152 at Lamptrai, 139 : preserves Zeuthen, H. G., 4 n. 2, 13, 13 n.4, work of Zenodorus, 139 16,17 n.24

249 o. Neugebauer A HISTORY OF ANCIENT MATHEMATICAL ASTRONOMY

(In. 3 parts, not available separately) 619 figures, 9 plates, 1 foldout. XXIII, VII, V, 1456 pages. 1975 (Studies in the and Physical Sciences)

Contents: The Almagest and its Direct Predecessors: Spherical As'tronomy. LunarTheory. Planetary Theory. Apollonius. Hipparchus.­ : Planetary Theory. Lunar Theory. Early Babylonian Astronomy. - Egypt. - Early Greek Astronomy: The Beginning of Greek Astronomy. Early Lunar and Solar Theory. Early Planetary Theory. The Development of Spherical Astronomy. - Astronomy during the Roman Imperial Period and Late Antiquity: Planetary and Lunar Theory before ptolemy. ptolemy's Minor Works and Related Thpics. The TIme from ptolemy to the Seventh Century. - Appendices and Indices: Chronological Concepts. Astronomical Concepts. Mathematical Concepts. Indices. Figures and Plates. This work covers the time from the beginnings of mathematical astronomy in Mesopotamia (fourth century B. C.) to the early Byzantine period (7th century A. D.). It is mainly concerned with the methods of representing and predicting lunisolar phenomena (e. g. eclipses) and planetary phases and positions, either by arithmetical methods or on the basis of kinematic models. Much attention is paid to auxiliary problems, e. g., spherical astronomy, mathematical geography, and numerical procedures. The goal of the work is twofold: first to give the reader a picture of the methods of approach to the fundamental problems faced by ancient astronomy, secondly to provide him with some insight into the source material, and its interpretation, on which our knowledge of ancient astronomy rests. In this way, it is hoped, he will not only be able to appreciate the enormous difficulties which had to be overcome to create a rational system of study of astronomy, but will also grasp the significance-of the study of astronomy for our understanding of far-reaching cultural Springer-Verlag relations in the ancient world and the Middle Ages. Berlin Great care has been taken to make details accessible through Heidelberg extensive indices and by references to the literature, ancient New York and modern.