INDEX OF GREEK WORDS AND FORMS.

  • ἀγώνιον, angle-less (figure) 187

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

  • ἀκιδοειδής, barb-like 188

  • ἄλογος, irrational: περὶ ἀλόγων γραμμῶν καὶ ναστῶν, work by Democritus 413

  • ἀμβλεῖα (γωνία), obtuse (angle) 181

  • ἀμβλυγώνιος, obtuse-angled 187

  • ἀμερής, indivisible 41, 268

  • ἀμφίκοιλος (of curvilineal angles) 178

  • ἀμφίκυρτος 178

  • ἀναγράφειν ἀπό to describe on contrasted with to construct (συστήσασθαι) 348

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

  • ἀναστροφικός (species of locus) 330

  • ἀνομοιομερής, non-uniform 40, 161–2

  • ἀντιστροφή, conversion 256–7: leading variety, ἡ προηγουμένη or ἡ κυρίως, ibid.

  • ἀνύπαρκτος, non-existent 129

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

  • ἀπαγωγή, reduction 135: εἰς τὸ ἀδύνατον 136

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

  • ἁπλοῦς, simple: (of lines or curves) 161–2: (of surfaces) 170

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

  • ἅπτεσθαι, to meet (occasionally touch) 57

  • ἄρρητος, irrational: of λόγος 137: of diameter (diagonal) 399

  • ἀσύμβατος, incompatible 129

  • ἀσύμπτωτος, not-meeting, non-secant, asymptotic 40, 161, 203

  • ἀσύνθετος, incomposite: (of lines) 160, 161: (of surfaces) 170

  • ἄτακτος, unordered: (of problems) 128: (of irrationals) 115

  • ἄτομοι γραμμαί, “indivisible lines” 268

  • αὐτὸς ἔφα, Ipse dixit, referring to Pythagoras 411

  • ἁψίς = segment of circle less than semicircle 187

  • βάθος, depth 158–9

  • βάσις, base 248–9

  • γαμήλιον διάγραμμα, “Figure of Marriage” (Plutarch), term for Pythagorean triangle (3, 4, 5), 417

  • γεγράφθω 242

  • γνώμων, see gnomon

  • γραμμή, line (or curve) q.v.

  • γραμμικῶς, graphically 400

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

  • δείγματα, illustrations, of Stoics 329

  • δεῖ δή, “thus it is required,” introducing διορισμός 293

  • διάγραμμα = proposition (Aristotle) 252

  • διαίρεσις: point of division (Aristotle) 165, 170, 171: method of division (exhaustion) 285: Euclid’s περὶ διαιρέσεων 8, 9, 18, 87, 110

  • διαστάσεις, almost = dimensions 157, 158

  • διαστατόν extended, ἐφ’ ἓν one way, ἐπὶ δύο two ways, ἐπὶ τρία three ways (of lines, surfaces and solids respectively) 158, 170

  • διάστημα, distance 166, 167, 207: (of radius of circle) 199: (of an angle) = divergence 176–7

  • διεξοδικός (of a class of loci) 330

  • διήχθω, “let it be drawn through” (= produced) 280

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

  • εἰσαγωγὴ ἁρμονική, Introduction to Harmony, by Cleonides 17

  • ἑκατέρα ἑκατέρᾳ, meaning respectively 248, 350

  • ἐκβεβλήσθωσαν, use of, 244

  • ἐκεῖνος = Euclid 400

  • ἔκθεσις, setting-out, one of formal divisions of proposition 129: sometimes omissible 130

  • ἐκτός, κατὰ τὸ (of an exterior angle in sense of re-entrant) 263: ἡ ἐκτὸς γωνία, the exterior angle 280

  • ἑλικοειδής, spiral-shaped 159

  • ἔλλειψις, falling-short (with reference to application of areas) 36, 343–5, 383–4

  • ἐλλιπὲς πρόβλημα, a deficient (= indeterminate) problem 129

  • ἐναλλάξ, alternately or (adjectivally) alternate 308

  • ἔννοια, notion, use of, 221

  • ἔνστασις, objection 135

  • ἐντός, κατὰ τὸ or ἡ ἐντὸς (γωνία) of an interior angle 263, 280: ἡ ἐντὸς καὶ ἀπεναντίον γωνία, the interior and opposite angle 280

  • ἐπεζεύχθωσαν (ἐπιζεύγνυμι, join) 242

  • ἐπίπεδον, plane in Euclid, used for surface also in Plato and Aristotle 169

  • ἐπιπροσθεῖν, ἐπίπροσθεν εἶναι, to stand in front of (hiding from view) 165, 166

  • ἐπιφάνεια, surface (Euclid) 169

  • ἑτερόμηκες, oblong 151, 188

  • εὐθύ, τό, the straight 159: εὐθεῖα (γραμμή), straight line 165–9

  • εὐθύγραμμος, rectilineal 187: neuter as substantive 346

  • ἐφάπτεσθαι, to touch 57

  • ἐφαρμόζειν, to coincide, ἐφαρμόζεσθαι, to be applied to 168, 224–5, 249

  • ἐφεκτικός (of a class of loci) 330

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

  • θεώρημα, theorem q.v.: θεώρημα τῆς νύμφης, “Theorem of the Bride,” = Eucl. I. 47, 417

  • θυρεός (shield) = ellipse 165

  • ἵππου πέδη (horse-fetter), name for a certain curve 162–3, 176

  • ἰσομέτρων σχημάτων, περί, on isometric figures (Zenodorus) 26, 27, 333

  • κάθετος εὐθεῖα γραμμή, perpendicular 181–2, 271: “plane” and “solid” 272

  • καθηγητής 20

  • καμπύλος, curved (of lines) 159

  • κατασκευή, construction, or machinery, one of divisions of a proposition 129: sometimes unnecessary 130

  • κατατομὴ κανόνος, Sectio canonis, attributed to Euclid 17

  • κείσθω, “let it be made” 269

  • κεκαμμένη, bent (of lines) 159, 176

  • κέντρον, centre 183, 184, 199: ἡ ἐκ τοῦ κέντρου = radius 199

  • κερατοειδής (γωνία), horn-like (angle) 177, 178, 182

  • κλᾶν, to inflect or deflect, κεκλᾶσθαι, κεκλασμένη, κλάσις 118, 150, 159, 176, 178

  • κλίσις, inclination, 176

  • κοιλογώνιον, hollow-angled figure (Zenodorus) 27, 188

  • κοιναὶ ἔννοιαι, Common Notions (= axioms) 221–2: called also τὰ κοινά, κοιναὶ δόξαι (Aristotle) 120, 221

  • κοινὴ προσκείσθω, ἀφῃρήσθω 276

  • κορυφή, vertex: κατὰ κορυφήν, vertical (angles) 278

  • κρίκος, ring (Heron) 163

  • λῆμμα, lemma (= something assumed, λαμβανόμενον) 133–4

  • λοιπός: λοιπὴ ἡ ΑΛ λοιπῇ τῇ ΒΗ ἴση ἐστίν 245

  • μέρη, parts (= direction) 190, 308, 323: (= side) 271

  • μῆκος, length, 158–9

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

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

  • μονὰς προσλαβοῦσα θέσιν, definition of a point 155

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

  • νεύσεις, inclinations, a class of problems 150–1: νεύειν, to verge 118, 150

  • ξυστροειδής, scraper-like (of angle) 178

  • ὁμοειδής, “of the same form” 250

  • ὅμοιος, “similar” (of numbers) 357: (of angles) = equal (Thales, Aristotle) 252

  • ὁμοιομερής, uniform (of lines or curves) 40, 161–2

  • ὀξεῖα (γωνία), acute (angle) 181

  • ὀξυγώνιος, acute-angled 187

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

  • ὀρθογώνιος, right-angled: as used of quadrilaterals = rectangular 188–9

  • ὅρος, ὁρισμός, definition 143: original meaning of ὅρος 143: = boundary, limit 182

  • ὄψις, visual ray 166

  • πάντῃ μεταλαμβανόμεναι, “taken together in any manner” 282

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

  • παράδοξος τόπος, ὁ, “the Treasury of Paradoxes” 329

  • παραλλάττω, “fall beside” or “awry” 262

  • παραπλήρωμα, complement, q.v.

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

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

  • περιφέρεια, circumference 184

  • περιφερής, circular 159

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

  • πλάτος, breadth 158–9

  • πλεονάζον (πρόβλημα), “(problem) in excess” 129

  • πόλος, a mathematical instrument 370

  • πολύπλευρον, many-sided figure 187

  • πορίσασθαι, to “find” or “furnish” 125

  • πόρισμα, porism q.v.

  • πρόβλημα, problem q.v.

  • προηγούμενος, leading: (of conversion) = complete 256–7: προηγούμενον (θεώρημα) leading (theorem) contrasted with converse 257

  • πρός, in geometry, various meanings 277

  • πρότασις, enunciation 129–30

  • προτείνω, “propound” 128

  • πρῶτος, prime, two senses of, 146

  • πτῶσις, case 134

  • ῥητός, rational 137: ῥητὴ διάμετρος τῆς πεμπάδος (“rational diameter of 5”) 399

  • σημεῖον, point 155–6

  • στάθμη, a mathematical instrument 371

  • στιγμή, point 156

  • στοιχεῖον, element 114–6

  • στρογγύλον, τό, round (circular), in Plato 159, 184: στρογγυλότης, roundness 182

  • συμπέρασμα, conclusion (of a proposition) 129, 130

  • σύνθετος, composite: (of lines or curves) 160: (of surfaces) 170

  • σύννευσις, convergence 282

  • συνίστασθαι, construct: special connotation 259, 289: with ἐντός 289: contrasted with παραβάλλειν (apply) 343

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

  • σχηματοποιοῦσα or σχῆμα ποιοῦσα, forming a figure (of a line or curve) 160–1

  • τεταγμένον (of a problem), “ordered” 128

  • τετραγωνισμός, squaring, definitions of 149–50, 410

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

  • τετράπλευρον, quadrilateral 187

  • τομή, section, = point of section 170, 171, 278

  • τοπικὸν θεώρημα, locus-theorem 329

  • τόπος: locus 329–31: room or space 23 n.: place (where things may be found), thus τόπος ἀναλυόμενος 8, 10: παράδοξος τόπος 329

  • τόρνος, instrument for drawing a circle 371

  • τρίπλευρον, three-sided figure 187

  • τυχὸν σημεῖον, a point at random 252

  • ὑπερβολή, exceeding, with reference to method of application of areas 36, 343–5, 386–7

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

  • ὑπόκειται, “is by hypothesis” 303, 312

  • ὑποτείνειν, subtend, with acc. or ὑπό and acc. 249, 283, 350

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