GENERAL INDEX OF GREEK WORDS
[The references are to volumes and pages.]
ȧyúviov, angle-less (figure) 1. 187 ἀδύνατον: ἡ εἰς τὸ ἀδ. ἀπαγωγή, ἡ διὰ τοῦ ἀδο δεῖξις, ἡ εἰς τὸ ἀδ. ἄγουσα ἀπόδειξις 1. 136 ákɩdoeɩôýs, barb-like 1. 188
xpos, extreme (of numbers in a series) II. 328, 367: (εἰς) ἄκρον καὶ μέσον λόγον TETμñolaι, "to be cut in extreme and mean ratio" II. 189
λoyos, having no ratio, irrational 11. 117-8: a relative term, resting on assumption or convention (Pythagoreans) III. I, II: use of term restricted in Euclid III. 12 iμßλeîa (ywría), obtuse (angle) 1. 181 ußλvywvios, obtuse-angled 1. 187 uepýs, indivisible I. 41, 268
upikoiλos (of curvilineal angles) 1. 178 upikupтos (of curvilineal angles) 1. 178 vayрápeш áπb, to describe on, contrasted with to construct (ovorno aolai) 1. 348: peculiar use of active participle, al toa τετράγωνα ἀναγράφουσαι = straight lines on which equal squares are described 111. 13 Evaλoyía, proportion: definitions of, inter- polated II. 119
Ενάλογον = ἀνὰ λόγον, proportional or in pro- portion: used as indeclinable adj. and as adv. II. 129, 165: μéon áváλoyov, mean proportional (of straight line) II. 129, similarly μέσος ἀνάλογον of numbers 1. 295, 363 etc.: τρίτη (τρίτος) ἀνάλογον, third proportional 11. 214, 407-8: TεтάрTη (τέταρτος) ἀνάλογον, fourth proportional II. 215, 409 : ἑξῆς ἀνάλογον, in continued proportion II. 346
vaλvóμevos (TÓπTOS), Treasury of Analysis, I. 8, 10, 11, 138
váπaλɩv (Xóyos), inverse (ratio), inversely II. 134
vаσтρéfavтi, convertendo, in proportions II. 135: analogous use otherwise than in proportions III. 164
vaσтρоon λoyov, "conversion" of a ratio II. 135 vаσтроДɩкós (species of locus) I. 330
ἀνισάκις ἀνισάκις ἴσος, unequal by unequal by equal (of solid numbers) = scalene, σφηνίσκος, σφηκίσκος οι βωμίσκος ΙΙ. 290 ȧvoμoloμeρns, non-uniform 1. 40, 161-2 ἀνομοίως τεταγμένων τῶν λόγων (of perturbed proportion) in Archimedes 11. 136 ἀνταναίρεσις, ἡ αὐτή, definition of same ratio in Aristotle (ávovpalpeois Alexander) II. 120 terms explained II. 121 ȧVTITETOVOÓTα σxhuara, reciprocal (= recipro- cally related) figures, interpolated def. of, II. 189
ȧvτLOTρоÓŃ, conversion 1. 256-7
leading variety, ή προηγουμένη or ή κυρίως, ibid. ȧvúжаρктоя, пon-existent 1. 129
ȧópioros, indeterminate: (of lines or curves) 1. 160: (of problems) 1. 129
ἀπαγωγή, reduction I. 135: εἰς τὸ ἀδύνατον I. 136
ἄπειρος, infinite: ἡ ἐπ ̓ ἄπ. ἐκβαλλομένη οι line or curve extending without limit and not "forming a figure" 1. 160-1: èπ'ǎπ. or εἰς ἄπ. adverbial I. 190: ἐπ' ἄπ. διαιρεῖσθαι I. 268: Aristotle on Tò &πepov 1. 232-4 ȧnλarns, breadthless: in definition of a line, μкоя ȧπλатés, breadthless length 1. 158: (of prime numbers) 11. 285
άλous, simple: (of lines or curves) 1. 161-2: (of surfaces) I. 170
ȧñódeižis, prvof (one of necessary divisions of a proposition) I. 129, 130 ȧTOKATAσTATIKÓS, recurrent (= spherical), of numbers II. 291
ȧπотоμn, apotome, a compound irrational, difference of two terms III. 7: defined III. 158-9: μέσης ἀποτομὴ πρώτη (δευτέρα), first (second) apotome of a medial (straight line) 111. 7, defined 111. 159-60 anтeσbal, to meet, occasionally to touch (instead of pánтeodai) 1. 57, II. 2: also =to pass through, to lie on II. 79 ȧpouós, number, definitions of, II. 280 appηTos, inexpressible, irrational: of Xoyos
άρTιоπéρITтos even-odd (Nicomachus etc.) 282
ἄρτιος (ἀριθμός), even (number) 11. 281 doúμßaros, incompatible 1. 129 ἀσύμμετρος, incommensurable: ἀ. μήκει (μόνον) incommensurable in length (only), dvváμei "in square" III. II
άσúμπтWтоя, not-meeting, non-secant, asym- ptotic 1. 40, 161, 203: (of parallel planes) III. 265 áσúvoεTOs, incomposite: (of lines) 1. 160, 161: (of surfaces) 1. 170: (prime and) incom- posite (of numbers) II. 284
άTaкTOS, unordered: (of problems) 1. 128: (of irrationals) I. 115, III. 10 ἄτομοι γραμμαί, "indivisible lines" 1. 268
Bálos, depth 1. 158-9
Báois, base 1. 248-9
Beẞnkéval, to stand (of angle standing on circumference) II. 4
Bwulokos, altar-shaped (of "scalene" solid numbers) 11. 290
yeyover (in constructions), "let it be (have been) made II. 248
γεγονὸς ἂν εἴη τὸ ἐπιταχθέν, “ what was
enjoined will have been done" II. 80, 261 yeypάpow, "let it be (lit. have been) drawn " I. 242
γενόμενος, ὁ ἐξ αὐτῶν, “their product II. 316, 326 etc.: ὁ ἐκ τοῦ ἑνὸς γενόμενος ="the square of the one" II. 327
μv, gnomon q.v.: Democritus Tepi dia- φορῆς γνώμονος (γνώμης or γωνίης ?) ἢ περὶ ψαύσιος κύκλου καὶ σφαίρης 11. 40: (of numbers) II. 289
Ypauun, line (or curve) q.v.
Ypauμikós, linear (of numbers in one dimen
sion) II. 287: (of prime numbers) II. 285: Ypaukus, graphically I. 400
Ypaperbaι, "to be proved" (Aristotle) II. 120
dedouévos, given, different senses I. 132-3: Euclid's dedouéva or Data q.v. delyuara, illustrations, of Stoics I. 329 deî dý, "thus it is required" (or "is neces- sary"), introducing dioptouós I. 293 DEUTEpos, secondary (of numbers): in Nico- machus and Iamblichus a subdivision of odd 11. 286, 287
dexóμevov, "admitting" (of segment of circle admitting or containing an angle) II. 5 diάypaμμa = proposition (Aristotle) 1. 252 diaipeio Pai (used of "separation" of ratios): διαιρεθέντα, separando, opp. to συγκείμενα, componendo 11. 168
dialpeois, point of division (Aristotle) 1. 165, 170, 171: method of division (exhaustion)
158, III. 262: Aristotle speaks of six διαστατόν, extended, ἐφ ̓ ἕν one way,
two ways, ènì тpia three ways (0 surfaces and solids respectively) 170, 111. 263 diáornua, distance 1. 166, 167, 207: (C of circle) 1. 199: (of an angle)=div 1. 176-7
διεζευγμένη αναλογία), disjoined (proportion) II. 293
die Nóvтi, separando, literally divide proportions) II. 135
dietodikos (of a class of loci) 1. 330 διῃρημένη (ἀναλογία), discrete (propor in four terms, as distinct from co- (συνεχής, συνημμένη) in three term
293 dinxow, "let it be drawn through
duced) or "across" I. 280, II. di' loov, ex aequali (of ratios) II.
ἴσου ἐν τεταραγμένῃ ἀναλογίᾳ, " ε. in perturbed proportion" 11. 136 dikóλoupos, twice-truncated (of F numbers) II. 291
duopio μós (1) particular statement tion, one of the formal divisions position 1. 129: (2) statement of of possibility I. 128, 129, 130, 243, 293 διπλάσιος λόγος, double ratio: διπλασ duplicate ratio, contrasted with, dúvams, power: actual value multiple in units (Nicomachus) = side of number not a compl. (i.e. root or surd) in Plato II. III. I, 2, 3: square in Plato II dúvaobai, "to be side of square
111. 13: αἱ δυνάμεναι αὐτά, sides equal to them III. 13: BI T δύναται τῇ ΔΖ, “the square greater than the square on A by on DF," literally BC is in po= than A by DF" III. 43
GENERAL INDEX OF GREEK WORDS AND FORMS
¿λáoσwv, minor (irrational) straight line 111. 7 etc.
EXKoeons, spiral-shaped 1. 159
Meiuua, defect (in application of areas) II. 262 EXλeiwew, "fall short" (in application of areas) II. 262
EXλes, falling-short (in application of areas) I. 36, 343-5, 383-4
Mès póẞnua, a deficient (= indetermi nate) problem 1. 129
EμπÍTTEш, fall in (= be interpolated) II. 358 évaλλáğ, alternately or (adjectivally) alternate
I. 308: évaλλàş λóyos, alternate ratio, alternando II. 134
Eva Tλelw, "several ones" (def. of number)
évapμóšew, to fit in (active) Book IV. Def. 7 and Prop. I, II. 79, 80, 81 Evvola, notion, use of, 1. 221 EvoTaois, objection 1. 135
EvTÓS, within (of internal contact of circles)
11. 13: κατὰ τὸ ἐντὸς or ἡ ἐντὸς (γωνία), οἱ an interior angle 1. 263, 280: ἡ ἐντὸς καὶ ἀπεναντίον γωνία, the interior and opposite angle 1. 280
és áváλoyov, in continued proportion (of terms in geometrical progression) II. 346 ἐπεζεύχθωσαν (ἐπιζεύγνυμι, join) I. 242 Émiμópios Móyos, superparticularis ratio=ratio (n + 1): n, II. 295
éπimedov, plane in Euclid, used for surface also in Plato and Aristotle 1. 169, III. 263 ἐπίπεδος (ἀριθμός), plane (number) 11. 287-8 ἐπιπροσθεῖν, ἐπίπροσθεν εἶναι, to stand in front of (hiding from view), in Plato's definitions of straight line and plane I. 165, 166
éπipáveia, surface: in Euclid 1. 169: in Aristotle III. 263
bueva, consequents (="following" terms) in a proportion II. 134, 238 ¿Teроμńκηs, oblong: éтepóμnkes, oblong (figure)
1. 151, 188: (of numbers) in Plato=πpo- μýκns, which however is distinguished from éтεроμńкпs by Nicomachus etc. II. 289-90, 293
εὐθύ, τὸ, the straight 1. 159: εὐθεῖα (γραμμή), straight line 1. 165-9
evovýраμμкós, rectilinear (term for prime numbers) II. 285
Evoúyрaμμos, rectilineal 1. 187: neuter as substantive 1. 346
EVOUμEтρIKós, euthymetric (of prime numbers) II. 285
éparтeσlai, to touch 1. 57
ἐφαρμόζειν, to coincide, ἐφαρμόζεσθαι, to be applied to 1. 168, 224-5, 249 ¿PEKTIKOS (of a class of loci) 1. 330 épens, "in order" 1. 181: of adjacent angles 1. 181, 278
youμeva, antecedents ("leading" terms) in a proportion II. 134
ἤπερ, than: construction after διπλασίων etc.
Oeúpnua, theorem, q.v.
Oupeós (shield) = ellipse 1. 165
idioμýкns, of square number (Iamblichus) 11. 293
inπоν Téon, hippopede (horse-fetter), name for a certain curve 1. 162-3, 176 ἰσάκις ἰσάκις ἴσος, equal multiplied by equal and again by equal (of a cube number) II. 290, 291
loákis loos, equal multiplied by equal (of a square number) 11. 291
ἰσάκις ἴσος ἐλαττονάκις (μειζονάκις), species of solid numbers, = πλινθίς (δοκίs or στηλίς) II. 291
ισομέτρων σχημάτων, περὶ, On isometric figures (Zenodorus) 1. 26, 27, 333
κάθετος εὐθεῖα γραμμή), perpendicular I. 181-2, 271: "plane" and "solid" per- pendicular I. 272
καλείσθω, "let it be called," indicating originality of a definition II. 129 KauжÚλos, curved (of lines) I. 159 κатаμетреv, measure II. 115: without re-
mainder," completely" (#λnpoúvτws) II. 280 κατασκευάζω, construct: τῶν αὐτῶν κατα- σKEVAσÔÉVTWV, "with the same construc- tion" II. 11
KaTaσKEVÝ, Construction, or machinery, one of the divisions of a proposition 1. 129: sometimes unnecessary I. 130 KaтaтоμỲ KаVÓvos, Sectio canonis of Euclid 1. 17, II. 295
Kelo0w, "let it be made I. 269 KEKаμμévη, bent (of lines) I. 159, 176 KÉVTρOV, centre 1. 183, 184, 199: of sphere ΙΙΙ. 270: ἡ ἐκ τοῦ κέντρου= radius 1. 199,
κερατοειδής (γωνία), horn-like (angle) 1. 177, 178, 182, II. 4, 39, 40
Klav, to break off, deflect, or inflect: KEKλáσOαι, def. of, alluded to by Aristotle 1. 118, 150, 176, 178, Ι. 47: κεκλασμένη γραμμή, defined by Heron 1. 150, 159: Kekλáσ0w δὴ πάλιν ΙΙ. 47
Kλáois, breaking (of lines) 1. 176 Kλios, inclination: (of line to line) 1. 176: (of straight line to plane or of plane to plane) III. 263-4: ὁμοίως κεκλίσθαι, to be similarly inclined III. 265 Koiλoyúviov, hollow-angled (figure), in Zeno- dorus 1. 27, 188
Koivai ěvvoiai, Common Notions (= axioms) 1. 221-2: called also τὰ κοινά, κοιναὶ δόξαι (Aristotle) 1. 120, 221
κοινὴ προσκείσθω, ἀφηρήσθω, “let there be added to, subtracted from, each" I. 276 Kown Toμn, common section (of planes) III. 263
Kóλoupos, truncated (of pyramidal number minus vertex) II. 291
Kopʊøý, vertex: Kaтà Kоρuþýν, vertical (angles) 1. 278
Kρikos, ring (Heron) 1. 163
Móyos, ratio: meaning II. 117: definition of, II. 116-9: original meaning (of something expressed) accounts for use of aλoyos, having no ratio, irrational 11. 117 λοιπός, remaining: λοιπὴ ἡ ΑΛ λοιπῇ τῇ ΒΗ ἴση ἐστίν 1. 245
μelswv, major (irrational straight line) III. 7, 87-8 etc.
μeμovŵobai, to be isolated, of μovás, unit (Theon of Smyrna) 11. 279
uépos, part: two meanings 11. 115: generally =submultiple 11. 280: μépn, parts (= proper fraction) 11. 115, 280: μépn (= direction) 1. 190, 308, 323: (=side) 1. 271 μέση ἀνάλογον (εὐθεῖα), μέσος ἀνάλογον (ἀριθ. μós), mean proportional (straight line or number) II. 129, 295, 363 etc. μéros, "medial" (of a certain irrational straight line or area) III. 49, 50: ʼn ék dúo μέσων πρώτη (δευτέρα), " the first (second) bimedial (straight line)" III. 7, 84-6: μέσης ἀποτομή πρώτη (δευτέρα), "first (second) apotome of a medial (straight line)” III. 7, 159–62: ῥητὸν καὶ μέσον duvaμévn, "side of (square equal to) the sum of a rational and a medial area 111. 7, 88-9: δύο μέσα δυναμένη, " side of the sum of two medial areas III. 7, 89-90 : ἡ μετὰ ῥητοῦ (μέσου) μέσον τὸ ὅλον TOLOUσa, "side of (square equal to) the difference between a medial and a rational (medial) area III. 7, 164-7
μETéwρos, elevated (above a plane) III. 272 μὴ γάρ, σε suppose it is not μкos, length 1. 158-9: in Plato
complete square or length commensurable with unit of length 11. 288, III. 3: more generally, of number in one dimension II. 287-8
μnvocions, lune-like (of angle) 1. 26, 201: Tò μηνοειδὲς (σχῆμα), lune 1. 187 MIKTÓS, "mixed" (of lines or curves) I. 161, 162 (of surfaces) 1. 170
μovás, unit, monad: supposed etymological connexion with μόνος, solitary, μονή, rest ΙΙ. 279 : μονὰς προσλαβοῦσα θέσιν, definition of a point 1. 155
μovóστpopos čλiğ, “single-turn spiral" 1. 122– 3 n., 164-5 in Pappus = cylindrical helix I. 165
vevoels, inclinations, a class of problems 1. 150-1: VEVEL, to verge 1. 118, 150 EvoτpоEidns, scraper-like (of angle) 1. 178 oμocions, "of the same form" I. 250
polated def. of proportion) II. 119 ouóλoyos, homologous, corresponding exceptionally "in the same rati 11. 238
ovoua, name or term, in such expre ἡ ἐκ δύο ὀνομάτων, the binomial line) III. 7 etc.
ὀξεία (γωνία), acute (angle) 1. 181 oğuyvios, acute-angled I. 187 ὅπερ ἔδει δεῖξαι (οι ποιῆσαι) Q.E.D. ( op@oywvios, right-angled: as used laterals = rectangular 1. 188-9 opiouós, definition I. 143 öpos, definition I. 143: original m I. 143 boundary, limit 1. 182 in a proportion II. 131 ofis, visual ray 1. 166
λeupá, side: (of factors of "plane" and "solid" numbers) 11. 288 πλῆθος ὡρισμένον οι πεπερασμένον, defined or finite multitude (definition of number) 11. 28ο: ἐκ μονάδων συγκείμενον πλῆθος (Euclid's def.) 11. 280
wo\λaw\aσiášeiv, multiply: defined 11. 287 πολλαπλασιασμός, multiplication: καθ' όποι- ονοῦν πολλαπλασιασμόν," (arising) from any multiple whatever" II. 120
πολλαπλάσιος, multiple: ισάκις πολλαπλάσια, equimultiples II. 120 etc.
Tóλos, a mathematical instrument 1. 370 πоλÚτλενрov, multilateral, many-sided figure I. 187: excludes Teтрáπλeupov, quadri- lateral II. 239
Topioaolai, to "find" or "furnish I. 125, II. 248
pioua, prism 111. 268 póßλnua, problem q.v. ponyoúμεvos, leading: (of conversion)= complete 1. 256-7: προηγούμενον (θεώρημα), leading (theorem), contrasted with converse 1.257
роμýкns, oblong (of numbers) in Plato = ἑτερομήκης, but distinguished from it by Nicomachus etc. II. 289-90, 293 rрós, in geometry, various meanings of, I. 277 pooavaypayaι, to draw on to: (of a circle) to complete, when segment is given II. 56 προσαρμόζουσα (εὐθεῖα) = “ annex,” the straight line which, when added to a compound ir- rational straight line formed by subtraction, makes up the greater "term," i.e. the negative "term III. 159 rpoσevpeiv, to find in addition (of finding third and fourth proportionals) II. 214 -póтaσis, enunciation 1. 129-30 -pоTeivw, to propound 1. 128
nueîov, point 1. 155-6
Orálun, a mathematical instrument 1. 371 σTEρEÓS, solid III. 262-3: of solid numbers II. 290-1: σTepeà ywvía, solid angle III. 2678: ὅμοια στερεά σχήματα, similar solid figures III. 265-7
σTYμń, point 1. 156
σTOXEîov, element 1. 114-6
σтроyyúλov, тò, the round (circular), in Plato I. 159, 184
στρογγυλότης, roundness 1. 182
σúμμεтρos, commensurable: μnkel, in length, duváμel μovov, in square only III. 11 σνμпéраσμа, conclusion (of a proposition) I. 129, 130
σúvevois, convergence I. 282
σUvexns, continuous : συνεχής αναλογία, "continuous proportion" (in three terms) 11. 131
ovrnuμévn åvaλoyla,connected (i.e. continuous) proportion II. 131, 293: σvvnμμévos of compound ratio in Archimedes II. 133 σvvlévтI, componendo II. 134-5
σúvbeσis Xóyov, "composition of a ratio," distinct from compounding of ratios 11. 134-5
TÚVOETOS, composite: (of lines or curves) 1. 160: (of surfaces) 1. 170: (of numbers), in Nicomachus and Iamblichus a sub- division of odd 11. 286
« ZurückWeiter » |