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| Heath T. — A History of Greek Mathematics, Vol. 2 |
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| Ïðåäìåòíûé óêàçàòåëü |
Mechanics, divisions of, writers on, Aristotle 344—346 445—446
Mechanics, divisions of, writers on, Heron ii. 346—352
Mechanics, divisions of, writers on, Pappus ii. 427—434
Mechanics, divisions of, writers on, Ptolemy ii. 295
Megethion ii. 360
Memus, Johannes Baptista ii. 127
Menaechmus 2 25 251—252 320—321
Menaechmus, discoverer of conic sections 251—253 ii.
Menaechmus, on 'problems' 318
Menaechmus, solved problem of two mean proportionals 245 246 251—255
Menelaus of Alexandria ii. 198 ii.
Menelaus of Alexandria, anharmonic property ii. 269
Menelaus of Alexandria, date ii. 260—261
Menelaus of Alexandria, Menelaus's theorem ii. 266—268 270
Menelaus of Alexandria, Sphaerica ii. 261—273
Menelaus of Alexandria, table of chords ii. 257
Mensa Pythagorea 47
Mensuration, in Egypt 122—128
Mensuration, in Heron ii. 316—335
Mensuration, in primary education 19
Meton 220
Metrodorus ii. 442
Minus, sign for, in Diophantus ii. 459—460
Mochus 4
Moschopoulos, Manuel ii. 549—550
Muhammad Bagdadinus 425
Multiplication table 53
Multiplication, 'Russian' method 53n.
Multiplication, Apollonius's continued multiplications 54—57
Multiplication, Egyptian method 52—53
Multiplication, examples from Eutocius, Heron, Theon 57—58
Multiplication, Greek method 53—54
Murran, an angular measure ii. 215
Musical intervals and numerical ratios 69 75—76 85 165
Myriads, 'first' second, notation for 39—40
Nagl, A. 50
Nasiraddin at-Tusi, version of Apollonius's Conics ii. 127
Nasiraddin at-Tusi, version of Euclid 362
Nasiraddin at-Tusi, version of Ptolemy ii. 275
Naucratis inscriptions 33
Nemesius 441
Neoclides 319
Ner (Babylonian) (=600) 28 ii.
Nesselmann, G.H.F. ii. 450—451 ii.
Newton 370 ii. ii.
Nicolas Rhabdas 40 ii. ii.
Nicomachus of Gerasa 12 69 70 72 73 74 76 83 85 86 ii. ii.
Nicomachus of Gerasa, Introductio arithmetica, character of treatise 98—99
Nicomachus of Gerasa, Introductio arithmetica, classification of numbers 99—100
Nicomachus of Gerasa, Introductio arithmetica, contents 99—112
Nicomachus of Gerasa, on 'perfect' numbers 74 100—101
Nicomachus of Gerasa, on a 'Platonic' theorem 297
Nicomachus of Gerasa, on ten means 87
Nicomachus of Gerasa, sum of series of natural cubes 109—110
Nicomachus of Gerasa, works of 97
Nicomedes 225—226 ii.
Nicomedes, cochloids or conchoids 238—240
Nicomedes, duplication of cube 260—262
Niloxenus 129
Nine, rule of 115—116
Nine, rule of, casting out nines ii. 549
Nipsus, M. Junius 132
Nix, L. ii. 128 131 ii.
Noeel, G. 282
Number, 'friendly' numbers 75
Number, 'oblong', 'prolate' 82—83 108 114
Number, 'oblong', 'prolate', similar plane and solid numbers 81—82 90
Number, 'oblong', 'prolate', solid numbers classified 106—108
Number, 'perfect', 'over-perfect' and 'defective' numbers 74—75
Number, 'the number in the heaven' (Pythagorean) 68
Number, 'the number in the heaven' (Pythagorean), 'number' of an object 69
Number, classification of numbers 70—74
Number, defined, by Moderatus, Eudoxus, Nicomachus, Aristotle 70
Number, defined, by Thales 69
Number, figured numbers 76—79
Numerals, Babylonian systems (1) decimal 28
Numerals, Babylonian systems (2) sexagesimal 28—29
Numerals, Egyptian 27—28
Numerals, Greek (1) 'Attic' or 'Herodianic' 30—31
Numerals, Greek (2) alphabetic system, original in Greece 31—37
Numerals, Greek (2) alphabetic system, original in Greece, comparison of two systems 37—39
Numerals, Greek (2) alphabetic system, original in Greece, date of introduction 33—35
Numerals, Greek (2) alphabetic system, original in Greece, how evolved 31—32
Numerals, Greek (2) alphabetic system, original in Greece, mode of writing 36—37
Numerals, notation for large numbers, Apollonius's tetrads 40
Numerals, notation for large numbers, Archimedes's octads 40—41
Numerals, origin of decimal system 26—27
Numerals, systems of, decimal, quinary, vigesimal 26
Nymphoclorus 213
Ocreatus 111
Octads, of Archimedes 40—41
Octagon, regular, area of ii. 328
octahedron 159 160 162
Octahedron, volume of ii. 335
Oenopides of Chios 22 121
Oenopides of Chios, called perpendicular gnomon-wise 78 175
Oenopides of Chios, discovered obliquity of ecliptic 138 174 ii.
Oenopides of Chios, Great Year of 174—175
Oenopides of Chios, two propositions in elementary geometry 175
Olympiodorus 444
One, the principle of number 69
Oppermann ii. 324n.
Optics, divisions of 17—18
Optics, of Euclid 441—444
Optics, of Ptolemy ii. 293—294
Oval of Cassini ii. 206
Oxyrhynchus Papyri 142
Pamphile 131 133 134
Pandrosion ii. 360
Pappus ii.17—18 ii. 180 181 182 183 185 186 187 188 189 190 ii. 211 212 213 ii. ii. ii.
Pappus, commentary on Euclid 358 ii.
Pappus, commentary on Euclid's Data 421—422 ii.
Pappus, commentary on Euclid's Data, on Diodorus's analemma ii. 287
Pappus, commentary on Euclid's Data, scholia on Syntaxis ii. 274
Pappus, commentary on Euclid, on Book X 154—155 209 211 ii.
Pappus, on 'Treasury of Analysis' 421 422 439 ii.
Pappus, on Apollonius's continued multiplications 54—57
Pappus, on Apollonius's tetrads 40
Pappus, on classification of problems and loci (plane, solid, linear) 218—219 ii.
Pappus, on classification of problems and loci (plane, solid, linear), criticism on Archimedes and Apollonius 288 ii. ii.
Pappus, on cochloids 238—239
Pappus, on conics of Euclid and Apollonius 438
Pappus, on conics of Euclid and Apollonius, proof of focus-directrix property ii. 120—121
Pappus, on duplication of cube 266—268 268—270
Pappus, on Euclid's Porisms 431—433 436—437 ii. ii.
Pappus, on isoperimetry (cf. Zenodorus) ii. 207 ii. ii.
Pappus, on mechanical works of Archimedes ii. 23—24
Pappus, on quadratrix 229—230 ii.
Pappus, on quadratrix, constructions for ii. 380—382
Pappus, on surface-loci 439—440 ii.
Pappus, on ten means 87—89
Pappus, on trisection of any angle 241—243 ii.
Parallelogram of velocities 346 ii.
Parapegma of Democritus 177
Parmenides 138
Paterius ii. 536—537
Patricius ii. 318 319
Pebbles, for calculation 46 48
Pentagon, regular, area of ii. 327
Pentagon, regular, construction Pythagorean 160—162
Pentagram, Pythagorean 161—162 see
Pericles 172
Pericles, a mathematician ii. 360
Perseus 226
Perseus, spiric sections ii. 203—206
Philippus of Opus 354
Philippus of Opus, astronomy 321
Philippus of Opus, on polygonal numbers 84 ii.
Philippus of Opus, works by 321
Philolaus 67 72 76 78 86 158 ii.
| Philolaus, on odd, even, and even-odd numbers 70—71
Philolaus, Pythagorean non-geocentric astronomy attributed to 163—164
Philon of Byzantium 213
Philon of Byzantium, duplication of cube 262—263
Philon of Gadara 234
Philon of Tyana ii. 260
Philon, Ctesibius and Heron ii. 298—302
Philoponus, Joannes 99 223 224n.
Phocaeans 7
Phocus of Samos 138
Phoenician alphabet, how treated by Greeks 31—32
Phoenician alphabet, how treated by Greeks, arithmetic originated with Phoenicians 120—121
Planisphaerium of Ptolemy ii. 292—293
Planudes, Maximus 117 ii. ii.
Plato 19 22 24 121 142n. 170 176
Plato, 'rational' and 'irrational diameter of 5' 93 306—307
Plato, a proposition in proportion 294
Plato, classification of numbers, odd, even 71—72 292
Plato, definitions of various species of numbers 292
Plato, definitions of various species of numbers, circle and sphere 293—294
Plato, definitions of various species of numbers, figure 292—293
Plato, definitions of various species of numbers, line and straight line 293
Plato, formula for rational right-angled triangles 81 304
Plato, hypotheses of mathematics 289—90
Plato, on 'perfect' proportion 86
Plato, on arithmetic and logistic 13—14
Plato, on arithmetical problems 15 ii.
Plato, on education in mathematics 19—20 284
Plato, on geometric means between two squares and two cubes respectively 89 112 201 297 400
Plato, On geometry 286—288
Plato, on mathematical 'arts', measurement and weighing 308
Plato, on mathematical 'arts', measurement and weighing, instruments for 308—309
Plato, on mathematical 'arts', measurement and weighing, principle of lever 309
Plato, on music 310
Plato, on number 5040 294
Plato, on optics 309 441
Plato, on points and indivisible lines 293
Plato, on regular and semi-regular solids 294—297
Plato, on solid geometry 12—13 303
Plato, ontology of mathematics 288—289
Plato, Plato and duplication of cube 245—246 255 287—288 303
Plato, Plato and the irrational 156 203—205 304
Plato, Plato's astronomy 310—315
Plato, propositions 'on the section' 304 324—325
Plato, supposed discovery of mathematical analysis 120 212—213 291—292
Plato, the geometrical number 305—308
Plato, two geometrical passages in Meno 297—303
Plato, two intellectual methods 290—292
Playfair, John 436
Pliny 129 ii.
Plutarch 84 96 128 129 130 133 144 145 167 179 ii. 3 ii.
Plutarch, On Archimedes ii. 17—18
Point, defined as a 'unit having position' 69 166
Point, Plato on points 293
Polybius 48 ii. ii.
Polygon, measurement of regular polygons ii. 326—329
Polygon, propositions about sum of exterior or interior angles 144
Polygonal numbers 15 76 79 ii. ii.
Polyhedra see "Solids"
Porism (1) = corollary 372
Porism (2) a certain type of proposition 373 431—438
Porism, Porism of Diophantus see "Diophantus"
Porism, Porisms of Euclid see "Euclid"
Porphyry 145
Porphyry, commentary on Euclid's Elements 358 ii.
Poselger, F.T. ii. 455
Posidonius ii. 219—222
Posidonius, definitions ii. 221 226
Posidonius, measurement of earth ii. 220
Posidonius, Meteorologica ii. 219
Posidonius, on parallels 358 ii.
Posidonius, on size of sun ii. 108 ii.
Posidonius, versus Zeno of Sidon ii. 221—222
Postulates, Aristotle on 336
Postulates, in Archimedes 336 ii.
Postulates, in Euclid 336 374—375
Powers, R.E. 75n.
Prestet, Jean 75n.
Prime numbers and numbers prime to one another 72—73
Prime numbers and numbers prime to one another, defined 73
Problems, classification 218—219
Problems, plane and solid ii. 117—118
Problems, problems and theorems 318 431 ii.
Proclus 12 99 175 183 213 224n. ii.
Proclus, 'summary' 118—121 170
Proclus, 'summary', object of 170—171
Proclus, attempt to prove parallel-postulate 358 ii.
Proclus, comm. on Eucl. I. ii. 530—535
Proclus, comm. on Republic 92—93 ii.
Proclus, Hypotyposis of astronomical hypotheses ii. 535—536
Proclus, on discoveries of Pythagoras 84—85 90 119 141 154
Proclus, on Euclid I. 47 145 147
Proclus, on Euclid's music 444
Proclus, on loci 219
Proclus, on porisms 433—434
Proclus, sources ii. 530—532
Prodicus, on secondary education 20—21
Prolate, of numbers 108 204
proof 370 ii.
Proportion, def. of numerical proportion 190
Proportion, Euclid's universally applicable theory due to Eudoxus 153 155 216 325—327
Proportion, the 'perfect' proportion 86
Proportion, theory discovered by Pythagoras 84—85
Proportion, theory discovered by Pythagoras, but his theory numerical and applicable to commensurables only 153 155 167
Proposition, geometrical, formal divisions of 370—371
Protagoras 202
Protagoras, on mathematics 23 179
Prou, V. ii. 309
Psammites or Sand-reckoner of Archimedes 40 ii. ii.
Psellus, Michael 223—224n. ii. ii.
Pseudaria of Euclid 430—431
Pseudo-Boeetius 47
Pseudo-Eratosthenes, letter on duplication of cube 244—245
Ptolemies, coins of, with alphabetic numerals 34—35
Ptolemies, Ptolemy I, story of 354
Ptolemy, Claudius 181 ii. ii. ii. ii.
Ptolemy, Claudius, analemma ii. 286—292
Ptolemy, Claudius, attempt to prove parallel-postulate 358 ii.
Ptolemy, Claudius, optics ii. 293—294
Ptolemy, Claudius, optics, other works ii. 293
Ptolemy, Claudius, Planispherium ii. 292—293
Ptolemy, Claudius, sexagesimal fractions 44—45
Ptolemy, Claudius, sexagesimal fractions, approximation to  233
Ptolemy, Claudius, Syntaxis ii. 273—286
Ptolemy, Claudius, Syntaxis, commentaries and editions ii. 274—275
Ptolemy, Claudius, Syntaxis, contents of ii. 275—276
Ptolemy, Claudius, Syntaxis, on obliquity of ecliptic ii. 107—108
Ptolemy, Claudius, Syntaxis, table of chords ii. 259 ii.
Ptolemy, Claudius, Syntaxis, trigonometry in ii. 276—286 290—291
Pyramids, measurement of height by Thales 129—130
Pyramids, measurements of, in Rhind Papyrus 126—128
Pyramids, origin of name 126
Pyramids, pyramids of Dakshur, Gizeh, and Medum 128
Pyramids, volume of pyramid 176 180 217 ii.
Pyramids, volume of pyramid, volume of frustum ii. 334
Pythagoras 65—66 121 131 133 138
Pythagoras, 'friendly' numbers 75
Pythagoras, arithmetic (theory of numbers) 66—80
Pythagoras, arithmetic (theory of numbers), figured numbers 76—79
Pythagoras, astronomy 162—163
Pythagoras, astronomy, independent movement of planets 67 163
Pythagoras, discovered dependence of musical intervals on numerical ratios 69 75—76 85 165
Pythagoras, formula for right-angled triangles in rational numbers 79—80
Pythagoras, founded theory of proportion 84—85
Pythagoras, founded theory of proportion, introduced 'perfect' proportion 86
Pythagoras, gnomons 77 79
Pythagoras, Heraclitus, Empedoeles and Herodotus on 65
Pythagoras, made mathematics a part of liberal education 141
Pythagoras, made mathematics a part of liberal education, called geometry 'inquiry' 166
Pythagoras, made mathematics a part of liberal education, used definitions 166
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