GENERAL INDEX OF GREEK WORDS AND FORMS.

[The references are to volumes and pages.]

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ἀγώνιον, angle-less (figure) I. 187

ἀδύνατον: ἡ εἰς τὸ ἀδ. ἀπαγωγή, ἡ διὰ τοῦ ἀδ. δεῖξις, ἡ εἰς τὸ ἀδ. ἄγουσα ἀπόδειξις I. 136

ἀκιδοειδής, barb-like I. 188

ἄκρος, extreme (of numbers in a series) II. 328, 367: (εἰς) ἄκρον καὶ μέσον λόγον τετμῆσθαι, “to be cut in extreme and mean ratio” II. 189

ἄλογος, having no ratio, irrational II. 117-8: a relative term, resting on assumption or convention (Pythagoreans) III. 1, 11: use of term restricted in Euclid III. 12

ἀμβλεῖα (γωνία), obtuse (angle) I. 181

ἀμβλυγώνιος, obtuse-angled I. 187

ἀμερής, indivisible I. 41, 268

ἀμφίκοιλος (of curvilineal angles) I. 178

ἀμφίκυρτος (of curvilineal angles) I. 178

ἀναγράφειν ἀπό, to describe on, contrasted with to construct (συστήσασθαι) I. 348: peculiar use of active participle; αἱ ἴσα τετράγωνα ἀναγράφουσαι = straight lines on which equal squares are described III. 13

ἀναλογία, proportion: definitions of, interpolated II. 119

ἀνάλογον = ἀνὰ λόγον, proportional or in proportion: used as indeclinable adj. and as adv. II. 129, 165: μέση ἀνάλογον, mean proportional (of straight line) II. 129, similarly μέσος ἀνάλογον of numbers II. 295, 363 etc.: τρίτη (τρίτος) ἀνάλογον, third proportional II. 214, 407-8: τετάρτη (τέταρτος) ἀνάλογον, fourth proportional II. 215, 409: ἑξῆς ἀνάλογον, in continued proportion II. 346

ἀναλυόμενος (τόπος), Treasury of Analysis, I. 8, 10, 11, 138

ἀνάπαλιν (λόγος), inverse (ratio), inversely II. 134

ἀναστρέψαντι, convertendo, in proportions II. 135: analogous use otherwise than in proportions III. 164

ἀναστροφὴ λόγου, “conversion” of a ratio II. 135

ἀναστροφικός (species of locus) I. 330

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ἀνισάκις ἀνισάκις ἴσος, unequal by unequal by equal (of solid numbers) = scalene, σφηνίσκος, σφηκίσκος or βωμίσκος II. 290

ἀνομοιομερής, non-uniform I. 40, 161-2

ἀνομοίως τεταγμένων τῶν λόγων (of perturbed proportion) in Archimedes II. 136

ἀνταναίρεσις, ἡ αὐτὴ, definition of same ratio in Aristotle (ἀνθυφαίρεσις Alexander) II. 120: terms explained II. 121

ἀντιπεπονθότα σχήματα, reciprocal (= reciprocally related) figures, interpolated def. of, II. 189

ἀντιστροφή, conversion I. 256-7: leading variety, ἡ προηγουμένη or ἡ κυρίως, ibid.

ἀνύπαρκτος, non-existent I. 129

ἄξων, axis III. 269

ἀόριστος, indeterminate: (of lines or curves) I. 160: (of problems) I. 129

ἀπαγωγή, reduction I. 135: εἰς τὸ ἀδύνατον I. 136

ἄπειρος, infinite: ἡ ἐπʼ ἄπ. ἐκβαλλομένη of line or curve extending without limit and not “forming a figure” I. 160-1: ἐπʼ ἄπ. or εἰς ἄπ. adverbial I. 190: ἐπʼ ἄπ. διαιρεῖσθαι I. 268: Aristotle on τὸ ἄπειρον I. 232-4

ἀπλατής, breadthless: in definition of a line, μῆκος ἀπλατές, breadthless length I. 158: (of prime numbers) II. 285

ἁπλοῦς, simple: (of lines or curves) I. 161-2: (of surfaces) I. 170

ἀπόδειξις, proof (one of necessary divisions of a proposition) I. 129, 130

ἀποκαταστατικός, recurrent (= spherical), of numbers II. 291

ἀποτομή, 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) III. 7, defined III. 159-60

ἅπτεσθαι, to meet, occasionally to touch (instead of ἐφάπτεσθαι) I. 57, II. 2: also = to pass through, to lie on II. 79

ἀριθμός, number, definitions of, II. 280

ἄρρητος, inexpressible; irrational: of λόγος <!– Column 1 –>

I. 137: ἄρρητος διάμετρος τῆς πεμπάδος, “irrational diameter of 5” (Plato) = $\sqrt{50}$, I. 399, III. 12, 525

ἀρτιάκις ἀρτιοδύναμον (Nicomachus) II. 282

ἀρτιάκις ἄρτιος, even-times even II. 281-2

ἀρτιάκις περισσός, even-times odd II. 282-4

ἀρτιοπέριττος even-odd (Nicomachus etc.) II. 282

ἄρτιος (ἀριθμός), even (number) II. 281

ἀσύμβατος, incompatible I. 129

ἀσύμμετρος, incommensurable: ἀ. μήκει (μόνον) incommensurable in length (only), δυνάμει “in square” III. 11

ἀσύμπτωτος, not-meeting, non-secant, asymptotic I. 40, 161, 203: (of parallel planes) III. 265

ἀσύνθετος, incomposite: (of lines) I. 160, 161: (of surfaces) I. 170: (prime and) incomposite (of numbers) II. 284

ἄτακτος, unordered: (of problems) I. 128: (of irrationals) I. 115, III. 10

ἄτομοι γραμμαί, “indivisible lines” I. 268

βάθος, depth I. 158-9

βάσις, base I. 248-9

βεβηκέναι, to stand (of angle standing on circumference) II. 4

βωμίσκος, altar-shaped (of “scalene” solid numbers) II. 290

γεγονέτω (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

γεγράφθω, “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

γνώμων, gnomon q.v.: Democritus περὶ διαφορῆς γνώμονος (γνώμης or γωνίης?) ἢ περὶ ψαύσιος κύκλου καὶ σφαίρης II. 40: (of numbers) II. 289

γραμμή, line (or curve) q.v.

γραμμικός, linear (of numbers in one dimension) II. 287: (of prime numbers) II. 285: γραμμικῶς, graphically I. 400

γράφεσθαι, “to be proved” (Aristotle) II. 120

δεδομένος, given, different senses I. 132-3: Euclid’s δεδομένα or Data q.v.

δείγματα, illustrations, of Stoics I. 329

δεῖ δή, “thus it is required” (or “is necessary”), introducing διορισμός I. 293

δεύτερος, secondary (of numbers): in Nicomachus and Iamblichus a subdivision of odd II. 286, 287

δεχόμενον, “admitting” (of segment of circle admitting or containing an angle) II. 5

διάγραμμα = proposition (Aristotle) I. 252

διαιρεῖσθαι (used of “separation” of ratios): διαιρεθέντι, separando, opp. to συγκείμενα, componendo II. 168

διαίρεσις, point of division (Aristotle) I. 165, 170, 171: method of division (exhaustion)

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I. 285: Euclid’s περὶ διαιρέσεων, On divisions (of figures) I. 8, 9, 18, 87, 110: διαίρεσις λόγου, separation, literally division, of ratio II. 135

διάμετρος, diameter: of a circle, parallelogram etc. I. 185, 325: of sphere III. 270

διαστάσεις, almost = “dimensions” I. 157, 158, III. 262: Aristotle speaks of six III. 263

διαστατόν, extended, ἐφʼ ἕν one way, ἐπὶ δύο two ways, ἐπὶ τρία three ways (of lines, surfaces and solids respectively) I. 158, 170, III. 263

διάστημα, distance I. 166, 167, 207: (of radius of circle) I. 199: (of an angle) = divergence I. 176-7

διεζευγμένη (ἀναλογία), disjoined = discrete (proportion) II. 293

διελόντι, separando, literally dividendo (of proportions) II. 135

διεξοδικός (of a class of loci) I. 330

διῃρημένη (ἀναλογία), discrete (proportion), i.e. in four terms, as distinct from continuous (συνεχής, συνημμένη) in three terms II. 131, 293

διήχθω, “let it be drawn through” (= produced) or “across” I. 280, II. 7

διʼ ἴσου, ex aequali (of ratios) II. 136: διʼ ἴσου ἐν τεταραγμένῃ ἀναλογίᾳ, “ex aequali in perturbed proportion” II. 136

δικόλουρος, twice-truncated (of pyramidal numbers) II. 291

διορισμός = (1) particular statement or definition, one of the formal divisions of a proposition I. 129: (2) statement of condition of possibility I. 128, 129, 130, 131, 234, 243, 293

διπλάσιος λόγος, double ratio: διπλασίων λόγος, duplicate ratio, contrasted with, II. 133

δύναμις, power: = actual value of a submultiple in units (Nicomachus) II. 282: = side of number not a complete square (i.e. root or surd) in Plato II. 288, 290, III. 1, 2, 3: = square in Plato II. 294-5

δύνασθαι, “to be side of square equal to” III. 13: αἱ δυνάμεναι αὐτά, sides of squares equal to them III. 13: ἡ ΒΓ τῆς Α μεῖζον δύναται τῇ ΔΖ, “the square on BC is greater than the square on A by the square on DF,” literally “BC is in power greater than A by DF” III. 43

εἶδος, figure II. 234: = form II. 254

εἰσαγωγὴ ἁρμονική, Introduction to Harmony, by Cleonides I. 17

ἕκαστος, each: curious use of, II. 79

ἑκατέρα ἑκατέρᾳ, meaning respectively I. 248, 350

ἐκβεβλήσθωσαν, use of, I. 244

ἐκεῖνος = Euclid I. 400

ἔκθεσις, setting-out, one of formal divisions of proposition I. 129: may sometimes be omitted I. 130

ἐκτός, κατὰ τὸ (of an exterior angle in sense of re-entrant) I. 263: ἡ ἐκτὸς γωνία, the exterior angle I. 280 <!– Column 1 –>

ἐλάσσων, minor (irrational) straight line III. 7 etc.

ἑλικοειδής, spiral-shaped I. 159

ἔλλειμμα, defect (in application of areas) II. 262

ἐλλείπειν, “fall short” (in application of areas) II. 262

ἔλλειψις, falling-short (in application of areas) I. 36, 343-5, 383-4

ἐλλιπὲς πρόβλημα, a deficient (= indeterminate) problem I. 129

ἐμπίπτειν, fall in (= be interpolated) II. 358

ἐναλλάξ, alternately or (adjectivally) alternate I. 308: ἐναλλὰξ λόγος, alternate ratio, alternando II. 134

ἕνα πλείω, “several ones” (def. of number) II. 280

ἐναρμόζειν, to fit in (active) Book IV. Def. 7 and Prop. 1, II. 79, 80, 81

ἔννοια, notion, use of, I. 221

ἔνστασις, objection I. 135

ἐντός, within: (of internal contact of circles) II. 13: κατὰ τὸ ἐντὸς or ἡ ἐντὸς (γωνία), of an interior angle I. 263, 280: ἡ ἐντὸς καὶ ἀπεναντίον γωνία, the interior and opposite angle I. 280

ἑξῆς ἀνάλογον, in continued proportion (of terms in geometrical progression) II. 346

ἐπεζεύχθωσαν (ἐπιζεύγνυμι, join) I. 242

ἐπιμόριος λόγος, superparticularis ratio = ratio $(n + 1) : n$, II. 295

ἐπίπεδον, plane in Euclid, used for surface also in Plato and Aristotle I. 169, III. 263

ἐπίπεδος (ἀριθμός), plane (number) II. 287-8

ἐπίπροσθεν, ἐπίπροσθεν εἶναι, to stand in front of (hiding from view), in Plato’s definitions of straight line and plane I. 165, 166

ἐπιφάνεια, surface: in Euclid I. 169: in Aristotle III. 263

ἑπόμενα, consequents (= “following” terms) in a proportion II. 134, 238

ἑτερομήκης, oblong: ἑτερόμηκες, oblong (figure) I. 151, 188: (of numbers) in Plato = προμήκης, which however is distinguished from ἑτερομήκης by Nicomachus etc. II. 289-90, 293

εὐθύ, τὸ, the straight I. 159: εὐθεῖα (γραμμή), straight line I. 165-9

εὐθύγραμμος, rectilinear (term for prime numbers) II. 285

εὐθύγραμμος, rectilineal I. 187: neuter as substantive I. 346

εὐθυμετρικός, euthymetric (of prime numbers) II. 285

ἐφάπτεσθαι, to touch I. 57

ἐφαρμόζειν, to coincide, ἐφαρμόζεσθαι, to be applied to I. 168, 224-5, 249

ἐφεκτικός (of a class of loci) I. 330

ἐφεξῆς, “in order” I. 181: of adjacent angles I. 181, 278

ἡγούμενα, antecedents (“leading” terms) in a proportion II. 134

ἤπερ, than: construction after διπλασίων etc. II. 133

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θεώρημα, theorem, q.v.

θυρεός (shield) = ellipse I. 165

ἰδιομήκης, of square number (Iamblichus) II. 293

ἵππου πέδη, hippopede (horse-fetter), name for a certain curve I. 162-3, 176

ἰσάκις ἰσάκις ἴσος, equal multiplied by equal and again by equal (of a cube number) II. 290, 291

ἰσάκις ἴσος, equal multiplied by equal (of a square number) II. 291

ἰσάκις ἴσος ἐλαττονάκις (μειζονάκις), species of solid numbers, = πλινθίς (δοκίς or στηλίς) II. 291

ἰσομέτρων σχημάτων, περὶ, On isometric figures (Zenodorus) I. 26, 27, 333

κάθετος (εὐθεῖα γραμμή), perpendicular I. 181-2, 271: “plane” and “solid” perpendicular I. 272

καθηγητής I. 20

καλείσθω, “let it be called,” indicating originality of a definition II. 129

καμπύλος, curved (of lines) I. 159

καταμετρεῖν, measure II. 115: without remainder, “completely” (πληρούντως) II. 280

κατασκευάζω, construct: τῶν αὐτῶν κατασκευασθέντων, “with the same construction” II. 11

κατασκευή, construction, or machinery, one of the divisions of a proposition I. 129: sometimes unnecessary I. 130

κατατομὴ κανόνος, Sectio canonis attributed to Euclid I. 17, II. 295

κείσθω, “let it be made” I. 269

κεκαμμένη, bent (of lines) I. 159, 176

κέντρον, centre I. 183, 184, 199: of sphere III. 270: ἡ ἐκ τοῦ κέντρου = radius I. 199, II. 2

κερατοειδὴς (γωνία), horn-like (angle) I. 177, 178, 182, II. 4, 39, 40

κλᾶν, to break off, deflect, or inflect: κεκλάσθαι, def. of, alluded to by Aristotle I. 118, 150, 176, 178, II. 47: κεκλασμένη γραμμή, defined by Heron I. 150, 159: κεκλάσθω δὴ πάλιν II. 47

κλάσις, breaking (of lines) I. 176

κλίσις, inclination: (of line to line) I. 176: (of straight line to plane or of plane to plane) III. 263-4: ὁμοίως κεκλίσθαι, to be similarly inclined III. 265

κοιλογώνιον, hollow-angled (figure), in Zenodorus I. 27, 188

κοιναὶ ἔννοιαι, Common Notions (= axioms) I. 221-2: called also τὰ κοινά, κοιναὶ δόξαι (Aristotle) I. 120, 221

κοινῇ προσκείσθω, ἀφῃρήσθω, “let there be added to, subtracted from, each” I. 276

κοινὴ τομή, common section (of planes) III. 263

κόλουρος, truncated (of pyramidal number minus vertex) II. 291

κορυφή, vertex: κατὰ κορυφήν, vertical (angles) I. 278

κρίκος, ring (Heron) I. 163 <!– Column 1 –>

κυκλικός, cyclic, a particular species of square number II. 291

κύλινδρος, cylinder III. 271

κῶνος, cone III. 270

λῆμμα, lemma (= something assumed, λαμβανόμενον) I. 133-4

λόγος, ratio: meaning II. 117: definition of, II. 116-9: original meaning (of something expressed) accounts for use of ἄλογος, having no ratio, irrational II. 117

λοιπός, remaining: λοιπὴ ἡ ΑΔ λοιπῇ τῇ ΒΗ ἴση ἐστίν I. 245

μείζων, major (irrational straight line) III. 7, 87-8 etc.

μεμονῶσθαι, to be isolated, of μονάς, unit (Theon of Smyrna) II. 279

μέρος, part: two meanings II. 115: generally = submultiple II. 280: μέρη, parts (= proper fraction) II. 115, 280: μέρη (= direction) I. 190, 308, 323: (= side) I. 271

μέση ἀνάλογον (εὐθεῖα), μέσος ἀνάλογον (ἀριθμός), mean proportional (straight line or number) II. 129, 295, 363 etc.

μέσος, “medial” (of a certain irrational straight line or area) III. 49, 50: ἡ ἐκ δύο μέσων πρώτη (δευτέρα), “the first (second) bimedial (straight line)” III. 7, 84-6: μέσης ἀποτομὴ πρώτη (δευτέρα), “first (second) apotome of a medial (straight line)” III. 7, 159-62: ῥητὸν καὶ μέσον δυναμένη, “side of (square equal to) the sum of a rational and a medial area” III. 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 ποιοῦσα, “side of (square equal to) the difference between a medial and a rational (medial) area III. 7, 164-7

μετέωρος, elevated (above a plane) III. 272

μὴ γάρ, “suppose it is not” II. 7

μῆκος, length I. 158-9: in Plato = side of complete square or length commensurable with unit of length II. 288, III. 3: more generally, of number in one dimension II. 287-8

μηνοειδής, lune-like (of angle) I. 26, 201: τὸ μηνοειδὲς (σχῆμα), lune I. 187

μικτός, “mixed” (of lines or curves) I. 161, 162: (of surfaces) I. 170

μονάς, unit, monad: supposed etymological connexion with μόνος, solitary, μονή, rest II. 279: μονὰς προσλαβοῦσα θέσιν, definition of a point I. 155

μονόστροφος ἕλιξ, “single-turn spiral” I. 122-3 n., 164-5: in Pappus = cylindrical helix I. 165

νεύσεις, inclinations, a class of problems I. 150-1: νεύειν, to verge I. 118, 150

ξυστροειδής, scraper-like (of angle) I. 178

ὁμοειδής, “of the same form” I. 250

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ὁμοιομερής, uniform (of lines or curves) I. 40, 161-2

ὅμοιος, similar: (of rectilineal figures) II. 188: (of angles) = equal (Thales, Aristotle) I. 252: (of segments of circles) II. 5; (of plane and solid numbers) I. 357, II. 293

ὁμοιότης λόγων, “similarity of ratios” (interpolated def. of proportion) II. 119

ὁμόλογος, homologous, corresponding II. 134: exceptionally “in the same ratio with” II. 238

ὄνομα, name or term, in such expressions as ἡ ἐκ δύο ὀνομάτων, the binomial (straight line) III. 7 etc.

ὀξεῖα (γωνία), acute (angle) I. 181

ὀξυγώνιος, acute-angled I. 187

ὅπερ ἔδει δεῖξαι (or ποιῆσαι) Q.E.D. (or F.) I. 57

ὀρθογώνιος, right-angled: as used of quadrilaterals = rectangular I. 188-9

ὁρισμός, definition I. 143

ὅρος, definition I. 143: original meaning of, I. 143: = boundary, limit I. 182: = term in a proportion II. 131

ὄψις, visual ray I. 166

πάντῃ μεταλαμβανόμεναι, “taken together in any manner” I. 282

παραβάλλειν, to apply (an area): παραβάλλειν ἀπό used, exceptionally, instead of παραβάλλειν παρὰ or ἀναγράφειν ἀπό II. 262

παραβολὴ τῶν χωρίων, application of areas I. 36, 343-5: contrasted with ὑπερβολή (exceeding) and ἔλλειψις (falling-short) I. 343: παραβολή contrasted with σύστασις (construction) I. 343: application of terms to conics by Apollonius I. 344-5

παράδοξος τόπος, ὁ, The Treasury of Paradoxes I. 329

παραλλάττω, “fall beside,” “sideways” or “awry” I. 262, II. 54

παραλληλεπίπεδος (adj.), parallelepipedal = “with parallel planes or faces”: στερεὸν παραλληλεπίπεδον = “parallelepipedal solid,” not “solid parallelepiped” III. 326

παραλληλόγραμμος, parallelogrammic (= parallel-lined): παραλληλόγραμμον χωρίον “parallelogrammic area,” shortened to παραλληλόγραμμον, parallelogram I. 325

παραπλήρωμα, complement (of a parallelogram) q.v.

πεντάγραμμον II. 99

περαίνουσα ποσότης, “limiting quantity” (Thymaridas’ definition of unit) II. 279

πέρας, extremity I. 165, 182: πέρας συγκλεῖον (Posidonius’ definition of figure) I. 183

περιεχομένη (of angle), περιεχόμενον (of rectangle), contained I. 370: τὸ δὶς περιεχόμενον, twice the rectangle contained I. 380: (of figure) contained or bounded I. 182, 183, 184, 186, 187

περισσάκις ἄρτιος, odd-times even II. 282-4

περισσάκις περισσός, odd-times odd II. 284

περισσάρτιος, odd-even (Nicomachus etc.) II. 283

περισσός, odd (number) II. 281 <!– Column 1 –>

περιφέρεια, circumference (includes arc) I. 184

περιφερής, circular I. 159

περιφερόγραμμος, contained by a circumference of a circle or by arcs of circles I. 182, 184

πηλίκος, how great: refers to continuous (geometrical) magnitude as ποσός to discrete (multitude) II. 116-7

πηλικότης, used in v. Def. 3 and vi. Def. 5: = size (not quantuplicity as it is translated by De Morgan) II. 116-7, 189-90: supposed multiplication of πηλικότητες (vi. Def. 5) II. 132: distinction between πηλικότης and μέγεθος II. 117

πλάτος, breadth I. 158-9: (of numbers) II. 288

πλεονάζον (πρόβλημα), “(problem) in excess” I. 129

πλευρά, side: (of factors of “plane” and “solid” numbers) II. 288

πλῆθος ὡρισμένον or πεπερασμένον, defined or finite multitude (definition of number) II. 280: ἐκ μονάδων συγκείμενον πλῆθος (Euclid’s def.) II. 280

πολλαπλασιάζειν, multiply: defined II. 287

πολλαπλασιασμός, multiplication: καθʼ ὁποιονοῦν πολλαπλασιασμόν, “(arising) from any multiple whatever” II. 120

πολλαπλάσιος, multiple: ἰσάκις πολλαπλάσια, equimultiples II. 120 etc.

πόλος, a mathematical instrument I. 370

πολύπλευρον, multilateral, many-sided figure I. 187: excludes τετράπλευρον, quadrilateral II. 239

πορίσασθαι, to “find” or “furnish” I. 125, II. 248

πόρισμα, porism q.v.

ποσάκις ποσάκις ποσοί, “so many times so many times so many” (of solid numbers, in Aristotle) II. 286, 290

ποσάκις ποσοί, “so many times so many” (of plane numbers, in Aristotle) II. 286

ποσόν, quantity, in Aristotle II. 115: refers to multitude as πηλίκον to magnitude II. 116-7

πρίσμα, prism III. 268

πρόβλημα, problem q.v.

προηγούμενος, leading: (of conversion) = complete I. 256-7: προηγούμενον (θεώρημα), leading (theorem), contrasted with converse I. 257

προμήκης, oblong (of numbers): in Plato = ἑτερομήκης, but distinguished from it by Nicomachus etc. II. 289-90, 293

πρός, in geometry, various meanings of, I. 277

προσαναγράψαι, 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 irrational straight line formed by subtraction, makes up the greater “term,” i.e. the negative “term” III. 159

προσευρεῖν, to find in addition (of finding third and fourth proportionals) II. 214

πρότασις, enunciation I. 129-30

προτείνω, to propound I. 128

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προτιθέναι, to propose: ἡ προτεθεῖσα εὐθεῖα, any assigned straight line III. 11

πρῶτοι πρὸς ἀλλήλους, (numbers) prime to one another II. 285-6

πρῶτος, prime: two senses of, I. 146: II. 284-5

πτῶσις, case I. 134

πυραμίς, pyramid III. 268

ῥητός, rational (literally “expressible”) I. 137, II. 117, III. 1: a relative term, unlike ἀσύμμετρος (incommensurable) which is a natural kind (Pythagoreans) III. 1: ῥητὴ διάμετρος τῆς πεμπάδος, “rational diameter of 5” (= 7, as approximation to $\sqrt{50}$) I. 399, III. 12, 525: ῥητὸν καὶ μέσον δυναμένη (= side of square equal to sum of a rational and a medial area) etc. III. 7

σημεῖον, point I. 155-6

στάθμη, a mathematical instrument I. 371

στερεός, solid III. 262-3: of solid numbers II. 290-1: στερεὰ γωνία, solid angle III. 267-8: ὅμοια στερεὰ σχήματα, similar solid figures III. 265-7

στιγμή, point I. 156

στοιχεῖον, element I. 114-6

στρογγύλον, τὸ, the round (circular), in Plato I. 159, 184

στρογγυλότης, roundness I. 182

σύμμετρος, commensurable: μήκει, in length, δυνάμει μόνον, in square only III. 11

συμπέρασμα, conclusion (of a proposition) I. 129, 130

σύνευσις, convergence I. 282

συνεχής, continuous: συνεχὴς ἀναλογία, “continuous proportion” (in three terms) II. 131

συνημμένη ἀναλογία, connected (i.e. continuous) proportion II. 131, 293: συνημμένος of compound ratio in Archimedes II. 133

συνθέντι, componendo II. 134-5

σύνθεσις λόγου, “composition of a ratio,” distinct from compounding of ratios II. 134-5

σύνθετος, composite: (of lines or curves) I. 160: (of surfaces) I. 170: (of numbers), in Nicomachus and Iamblichus a subdivision of odd II. 286

συνίστασθαι, construct: special connotation I. 259, 289: with ἐντός I. 289: contrasted with παραβάλλειν (apply) I. 343: οὐ συσταθήσεται, συσταθήσονται, “there cannot be constructed” I. 259, II. 53

συντίθημι, σύγκειμαι (of ratios) II. 135, 189-90: συγκείμενα and διαιρεθέντα (componendo and separando) used relatively to one another II. 168, 170

σύστημα μονάδων, “collection of units” (def. of number) II. 280

συστηματικός, collective II. 279

σφαῖρα, sphere III. 269

σφαιρικός, spherical (of a particular species of cube number) II. 291

σφηνίσκος or σφηκίσκος, of solid number with all three sides unequal (= scalene) II. 290 <!– Column 1 –>

σχέσις, “relation”: ποιὰ σχέσις, “a sort of relation” (in def. of ratio) II. 116-7

σχηματογραφεῖν, σχηματογραφία, representing (numbers) by figures of like shape I. 359

σχηματοποιοῦσα or σχῆμα ποιοῦσα, “forming a figure” (of a line or curve) I. 160-1

ταυτομήκης, of square number (Nicomachus) II. 293

ταὐτότης λόγων, “sameness of ratios” II. 119

τέλειος, perfect (of a class of numbers) II. 293-4

τεταγμένος, “ordered”: τεταγμένον πρόβλημα, “ordered” problem I. 128: τεταγμένη ἀναλογία, “ordered” proportion II. 137

τεταραγμένη ἀναλογία, perturbed proportion II. 136

τετραγωνισμός, squaring, definitions of, I. 149-50, 410

τετράγωνον, square: sometimes (but not in Euclid) any four-angled figure I. 188

τετράπλευρον, quadrilateral I. 187: not a “polygon” II. 239

τμῆμα κύκλου, segment of a circle: τμήματος γωνία, angle of a segment II. 4: ἐν τμήματι γωνία, angle in a segment II. 4

τομεὺς (κύκλου), sector (of a circle): σκυτοτομικὸς τομεύς, “shoemaker’s knife” II. 5

τομή, section, = point of section I. 170, 171, 278: κοινὴ τομή, “common section” III. 263

τομοειδής (of figure), sector-like II. 5

τοπικὸν θεώρημα, locus-theorem I. 329

τόπος, locus I. 329-31: = room or space I. 23 n.: place (where things may be found), thus τόπος ἀναλυόμενος, Treasury of Analysis I. 8, 10, παράδοξος τόπος, Treasury of Paradoxes, I. 329

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τόρνος, instrument for drawing a circle I. 371

τοσαυταπλάσιον, “the same multiple” II. 146

τρίγωνον, triangle: τὸ τριπλοῦν, τὸ διʼ ἀλλήλων, triple, interwoven triangle, = pentagram II. 99

τριπλάσιος, triple, τριπλασίων, triplicate (of ratios) II. 133

τρίπλευρον, three-sided figure I. 187

τυγχάνειν, happen: τυχὸν σημεῖον, any point at random I. 252: τυχοῦσα γωνία, “any angle” II. 212: ἄλλα, ἃ ἔτυχεν, ἰσάκις πολλαπλάσια, “other, chance, equimultiples” II. 143-4

ὑπερβολή, exceeding, with reference to method of application of areas I. 36, 343-5, 386-7

ὑπερτελής or ὑπερτέλειος, “over-perfect” (of a class of numbers) II. 293-4

ὑπό, in expressions for an angle (ἡ ὑπὸ ΒΑΓ γωνία) I. 249, and a rectangle I. 370

ὑποδιπλάσιος, sub-duplicate, = half (Nicomachus) II. 280

ὑποκείμενος, laid down or assumed: τὸ ὑποκείμενον ἐπίπεδον, the plane of reference III. 272

ὑπόκειται, “is by hypothesis” I. 303, 312

ὑποπολλαπλάσιος, submultiple (Nicomachus) II. 280

ὑποτείνειν, subtend, with acc. or ὑπὸ and acc. I. 249, 283, 350

ὕψος, height II. 189

χωρίον, area II. 254

ὡρισμένη γραμμή, determinate line (curve), “forming a figure” I. 160