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GENERAL INDEX OF GREEK WORDS

AND FORMS.

[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

H. E. III.

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

ǎwv, axis III. 269

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

34

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

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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

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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)

II. 280

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.

11. 133

Oeúpnua, theorem, q.v.

Oupeós (shield) = ellipse 1. 165

531

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

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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,

II. 2

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

66

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

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μETéwρos, elevated (above a plane) III. 272
μὴ γάρ, σε suppose it is not
μкos, length 1. 158-9: in Plato

II. 7

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side of

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

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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

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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

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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

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