Principia

Index

Contents

All of the Latin is here. ◆ marks a unit with full English annotation; ◇ marks Latin with only a section headnote so far.

ProlegomenaFront matter, definitions and laws

Titulus, Dedicatio, Præfatio, Carmen Title page, dedication, preface and Halley’s ode annotated
  1. ◆ Titulus
  2. ◆ Dedicatio
  3. ◆ Præfatio ad Lectorem
  4. ◆ Halley’s ode: In viri præstantissimi D. Isaaci Newtoni opus
Definitiones Definitions pp. 1–12 annotated
  1. ◆ Def. I p. 1
  2. ◆ Def. II p. 2
  3. ◆ Def. III p. 2
  4. ◆ Def. IV p. 2
  5. ◆ Def. V p. 3
  6. ◆ Def. VI p. 3
  7. ◆ Def. VII p. 3
  8. ◆ Def. VIII p. 3
  9. ◆ Scholium p. 5
Axiomata, sive Leges Motus Axioms, or Laws of Motion pp. 12–26 annotated
  1. ◆ Lex. I p. 12
  2. ◆ Lex. II p. 12
  3. ◆ Lex. III p. 13
  4. ◆ Corol. I p. 13
  5. ◆ Corol. II p. 14
  6. ◆ Corol. III p. 16
  7. ◆ Corol. IIII p. 17
  8. ◆ Corol. V p. 19
  9. ◆ Corol. VI p. 20
  10. ◆ Scholium p. 20

De Motu Corporum, Liber PrimusBook I · The motion of bodies

Liber Primus, Sect. I. De Methodo Rationum primarum & ultimarum, cujus ope sequentia demonstrantur. Book I, Section I pp. 26–37 annotated
  1. ◆ LEMMA I p. 26
  2. ◆ Lemma II p. 27
  3. ◆ Lemma III p. 27
  4. ◆ Lemma IV p. 28
  5. ◆ Lemma V p. 29
  6. ◆ Lemma VI p. 29
  7. ◆ Lemma VII p. 30
  8. ◆ Lemma VIII p. 30
  9. ◆ Lemma IX p. 31
  10. ◆ Lemma X p. 32
  11. ◆ Lemma XI p. 32
  12. ◆ Scholium p. 34
Liber Primus, Sect. II. De Inventione Virium Centripetarum. Book I, Section II pp. 37–50 annotated
  1. ◆ Prop. I. Theorema. I p. 37
  2. ◆ Pro. II. Theor. II p. 38
  3. ◆ Scholium p. 39
  4. ◆ Prop. III. Theor. III p. 39
  5. ◆ Scholium p. 40
  6. ◆ Prop. IV. Theor. IV p. 41
  7. ◆ Scholium p. 42
  8. ◆ Prop. V. Prob. I p. 43
  9. ◆ Pro. VI. Theor. V p. 44
  10. ◆ Prop. VII. Prob. II p. 45
  11. ◆ Prop. VIII. Prob. III p. 46
  12. ◆ Scholium p. 47
  13. ◆ Prop. IX. Prob. IV p. 47
  14. ◆ Lemma XII p. 47
  15. ◆ Prop. X. Prob. V p. 48
  16. ◆ Scholium p. 49
Liber Primus, Sect. III. De motu Corporum in Conicis Sectionibus excentricis. Book I, Section III pp. 50–61 annotated
  1. ◆ Prop. XI. Prob. VI p. 50
  2. ◆ Prop. XII. Prob. VII p. 51
  3. ◆ Lemma XIII p. 53
  4. ◆ Lemma XIV p. 53
  5. ◆ Prop. XIII. Prob. VIII p. 54
  6. ◆ Prop. XIV. Theor. VI p. 55
  7. ◆ Prop. XV. Theor. VII p. 56
  8. ◆ Prop. XVI. Theor. VIII p. 56
  9. ◆ Prop. XVII. Prob. IX p. 58
Liber Primus, Sect. IV. De Inventione Orbium Ellipticorum, Parabolicorum & Hyperbolicorum ex umbilico dato. Book I, Section IV pp. 61–70 annotation forthcoming
  1. ◇ Lemma XV p. 61
  2. ◇ Prop. XVIII. Prob. X p. 61
  3. ◇ Prop. XIX. Prob. XI p. 62
  4. ◇ Prop. XX. Prob. XII p. 63
  5. ◇ Lemma XVI p. 67
  6. ◇ Prop. XXI. Prob. XIII p. 68
  7. ◇ Scholium p. 68
Liber Primus, Sect. V. Inventio orbium ubi umbilicus neuter datur. Book I, Section V pp. 70–104 annotation forthcoming
  1. ◇ Lemma XVII p. 70
  2. ◇ Lemma XVIII p. 72
  3. ◇ Scholium p. 73
  4. ◇ Lemma XIX p. 74
  5. ◇ Lemma XX p. 75
  6. ◇ Lemma XXI p. 77
  7. ◇ Prop. XXII. Prob. XIV p. 79
  8. ◇ Idem aliter p. 80
  9. ◇ Schol p. 81
  10. ◇ Prop. XXIII. Prob. XV p. 81
  11. ◇ Idem aliter p. 82
  12. ◇ Prop. XXIV. Prob. XVI p. 84
  13. ◇ Lemma XXII p. 85
  14. ◇ Prop. XXV. Prob. XVII p. 87
  15. ◇ Prop. XXVI. Prob. XVIII p. 89
  16. ◇ Lemma XXIII p. 89
  17. ◇ Lemma XXIV p. 90
  18. ◇ Lemma XXV p. 91
  19. ◇ Prop. XXVII. Prob. XIX p. 92
  20. ◇ Schol p. 94
  21. ◇ Lemma XXVI p. 95
  22. ◇ Prop. XXVIII. Prob. XX p. 97
  23. ◇ Lemma XXVII p. 98
  24. ◇ Prop. XXIX. Prob. XIX p. 102
  25. ◇ Scholium p. 103
Liber Primus, Sect. VI. De inventione motuum in Orbibus datis. Book I, Section VI pp. 104–115 annotation forthcoming
  1. ◇ Prop. XXX. Prob. XXII p. 104
  2. ◇ Lemma XXVIII p. 105
  3. ◇ Corollarium p. 107
  4. ◇ Prop. XXXI. Prob. XXIII p. 107
  5. ◇ Scholium p. 109
Liber Primus, Sect. VII. De Corporum Ascensu & Descensu Rectilineo. Book I, Section VII pp. 115–125 annotation forthcoming
  1. ◇ Prop. XXXII. Prob. XXIV p. 115
  2. ◇ Prop. XXXIII. Theor. IX p. 116
  3. ◇ Prop. XXXIV. Theor. X p. 118
  4. ◇ Prop. XXXV. Theor. XI p. 118
  5. ◇ Prop. XXXVI. Prob. XXV p. 120
  6. ◇ Prop. XXXVII. Prob. XXVI p. 120
  7. ◇ Prop. XXXVIII. Theor. XII p. 121
  8. ◇ Prop. XXXIX. Prob. XXVII p. 122
Liber Primus, Sect. VIII. De Inventione Orbium in quibus corpora viribus quibuscunq; centripetis agitata revolventur. Book I, Section VIII pp. 125–132 annotation forthcoming
  1. ◇ Prop. XL. Theor. XIII p. 125
  2. ◇ Prop. XLI. Prob. XXVIII p. 127
  3. ◇ Prop. XLII. Prob. XXIX p. 131
Liber Primus, Sect. IX. De Motu Corporum in Orbibus mobilibus, deq; motu Apsidum. Book I, Section IX pp. 132–145 annotation forthcoming
  1. ◇ Prop. XLIII. Prob. XXX p. 132
  2. ◇ Prop. XLIV. Theor. XIV p. 133
  3. ◇ Prop. XLV. Prob. XXXI p. 137
Liber Primus, Sect. X. De Motu Corporum in Superficiebus datis, deq; Funipendulorum Motu reciproco. Book I, Section X pp. 145–162 annotation forthcoming
  1. ◇ Prop. XLVI. Prob. XXXII p. 145
  2. ◇ Prop. XLVII. Theor. XV p. 146
  3. ◇ Scholium p. 147
  4. ◇ Prop. XLVIII. Theor. XVI p. 147
  5. ◇ Prop. XLIX. Theor. XVII p. 147
  6. ◇ Prop. L. Prob. XXXIII p. 150
  7. ◇ Prop. LI. Theor. XVIII p. 151
  8. ◇ Prop. LII. Prob. XXXIV p. 153
  9. ◇ Prop. LIII. Prob. XXXV p. 157
  10. ◇ Prop. LIV. Prob. XXXVI p. 158
  11. ◇ Prop. LV. Theor. XIX p. 159
  12. ◇ Prop. LVI. Prob. XXXVII p. 161
Liber Primus, Sect. XI. De Motu Corporum Sphæricorum viribus centripetis se mutuo petentium. Book I, Section XI pp. 162–192 annotation forthcoming
  1. ◇ Prop. LVII. Theor. XX p. 162
  2. ◇ Prop. LVIII. Theor. XXI p. 163
  3. ◇ Prop. LIX. Theor. XXII p. 165
  4. ◇ Prop. LX. Theor. XXIII p. 166
  5. ◇ Prop. LXI. Theor. XXIV p. 167
  6. ◇ Prop. LXII. Prob. XXXVIII p. 168
  7. ◇ Prop. LXIII. Prob. XXXIX p. 168
  8. ◇ Prop. LXIV. Prob. XL p. 169
  9. ◇ Prop. LXV. Theor. XXV p. 170
  10. ◇ Prop. LXVI. Theor. XXVI p. 173
  11. ◇ Prop. LXVII. Theor. XXVII p. 188
  12. ◇ Prop. LXVIII. Theor. XXVIII p. 188
  13. ◇ Prop. LXIX. Theor. XXIX p. 190
  14. ◇ Scholium p. 191
Liber Primus, Sect. XII. De Corporum Sphæricorum Viribus attractivis. Book I, Section XII pp. 192–213 annotation forthcoming
  1. ◇ Prop. LXX. Theor. XXX p. 192
  2. ◇ Prop. LXXI. Theor. XXXI p. 193
  3. ◇ Prop. LXXII. Theor. XXXII p. 195
  4. ◇ Prop. LXXIII. Theor. XXXIII p. 196
  5. ◇ Scholium p. 196
  6. ◇ Prop. LXXIV. Theor. XXXIV p. 197
  7. ◇ Prop. LXXV. Theor. XXXV p. 197
  8. ◇ Prop. LXXVI. Theor. XXXVI p. 198
  9. ◇ Prop. LXXVII. Theor. XXXVII p. 200
  10. ◇ Prop. LXXVIII. Theor. XXXVIII p. 202
  11. ◇ Scholium p. 203
  12. ◇ Lemma XXIX p. 203
  13. ◇ Prop. LXXIX. Theor. XXXIX p. 204
  14. ◇ Prop. LXXX. Theor. XL p. 205
  15. ◇ Prop. LXXXI. Prob. XLI p. 206
  16. ◇ Prop. LXXXII. Theor. XLI p. 210
  17. ◇ Prop. LXXXIII. Prob. XLII p. 212
  18. ◇ Prop. LXXXIV. Prob. XLIII p. 212
  19. ◇ Scholium p. 213
Liber Primus, Sect. XIII. De Corporum etiam non Sphæricorum viribus attractivis. Book I, Section XIII pp. 213–227 annotation forthcoming
  1. ◇ Prop. LXXXV. Theor. XLII p. 213
  2. ◇ Prop. LXXXVI. Theor. XLIII p. 214
  3. ◇ Prop. LXXXVII. Theor. XLIV p. 215
  4. ◇ Prop. LXXXVIII. Theor. XLV p. 216
  5. ◇ Prop. LXXXIX. Theor. XLVI p. 217
  6. ◇ Prop. XC. Prob. XLIV p. 218
  7. ◇ Prop. XCI. Prob. XLV p. 219
  8. ◇ Prop. XCII. Prob. XLVI p. 222
  9. ◇ Prop. XCIII. Theor. XLVII p. 223
  10. ◇ Scholium p. 225
Liber Primus, Sect. XIV. De motu corporum minimorum, quæ viribus centripetis ad singulas magni alicujus corporis partes tendentibus agitantur. Book I, Section XIV pp. 227–236 annotation forthcoming
  1. ◇ Prop. XCIV. Theor. XLVIII p. 227
  2. ◇ Prop. XCV. Theor. XLIX p. 229
  3. ◇ Prop. XCVI. Theor. L p. 230
  4. ◇ Scholium p. 231
  5. ◇ Prop. XCVII. Prob. XLVII p. 232
  6. ◇ Prop. XCVIII. Prob. XLVIII p. 233
  7. ◇ Scholium p. 234

De Motu Corporum, Liber SecundusBook II · Motion in resisting media

Liber Secundus, Sect. I. De Motu corporum quibus resistitur in ratione velocitatis. Book II, Section I pp. 236–246 annotation forthcoming
  1. ◇ Prop. I. Theor. I p. 236
  2. ◇ Lemma I p. 237
  3. ◇ Prop. II. Theor. II p. 237
  4. ◇ Prop. III. Prob. I p. 238
  5. ◇ Prop. IV. Prob. II p. 241
  6. ◇ Scholium p. 245
Liber Secundus, Sect. II. De motu corporum quibus resistitur in duplicata ratione velocitatum. Book II, Section II pp. 246–274 annotation forthcoming
  1. ◇ Prop. V. Theor. III p. 246
  2. ◇ Prop. VI. Theor. IV p. 248
  3. ◇ Prop. VII. Theor. V p. 249
  4. ◇ Lemma II p. 250
  5. ◇ Scholium p. 253
  6. ◇ Prop. VIII. Theor. VI p. 254
  7. ◇ Prop. IX. Theor. VII p. 256
  8. ◇ Prop. X. Prob. III p. 260
  9. ◇ Scholium p. 269
Liber Secundus, Sect. III. De motu corporum quæ resistuntur partim in ratione velocitatis, partim in ejusdem ratione duplicata. Book II, Section III pp. 274–283 annotation forthcoming
  1. ◇ Prop. XI. Theor. VIII p. 274
  2. ◇ Prop. XII. Theor. IX p. 276
  3. ◇ Prop. XIII. Theor. X p. 277
  4. ◇ Prop. XIV. Prob. IV p. 280
Liber Secundus, Sect. IV. De Corporum circulari Motu in Mediis resistentibus. Book II, Section IV pp. 283–290 annotation forthcoming
  1. ◇ LEM. III p. 283
  2. ◇ Prop. XV. Theor. XI p. 284
  3. ◇ Prop. XVI. Theor. XII p. 288
  4. ◇ Scholium p. 289
  5. ◇ Prop. XVII. Prob. V p. 289
  6. ◇ Prop. XVIII. Prob. VI p. 289
Liber Secundus, Sect. V. De Densitate & compressione Fluidorum, deque Hydrostatica. Book II, Section V pp. 290–303 annotation forthcoming
  1. ◇ Definitio Fluidi p. 290
  2. ◇ Prop. XIX. Theor. XIII p. 290
  3. ◇ Prop. XX. Theor. XIV p. 292
  4. ◇ Prop. XXI. Theor. XV p. 296
  5. ◇ Prop. XXII. Theor. XVI p. 298
  6. ◇ Scholium p. 300
  7. ◇ Prop. XXIII. Theor. XVII p. 301
  8. ◇ Scholium p. 302
Liber Secundus, Sect. VI. De Motu & resistentia Corporum Funependulorum. Book II, Section VI pp. 303–317 annotation forthcoming
  1. ◇ Prop. XXIV. Theor. XVIII p. 303
  2. ◇ Prop. XXV. Theor. XIX p. 305
  3. ◇ Prop. XXVI. Theor. XX p. 307
  4. ◇ Prop. XXVII. Theor. XXI p. 307
  5. ◇ Prop. XXVIII. Theor. XXII p. 308
  6. ◇ Prop. XXIX. Prob. VII p. 309
  7. ◇ Prop. XXX. Theor. XXIII p. 312
  8. ◇ Prop. XXXI. Theor. XXIV p. 315
Liber Secundus, Sect. VII. De Motu Fluidorum & resistentia Projectilium. Book II, Section VII pp. 317–354 annotation forthcoming
  1. ◇ Prop. XXXII. Theor. XXV p. 317
  2. ◇ Prop. XXXIII. Theor. XXVI p. 319
  3. ◇ Prop. XXXIV. Theor. XXVII p. 323
  4. ◇ Prop. XXXV. Theor. XXVIII p. 324
  5. ◇ Scholium p. 326
  6. ◇ Prop. XXXVI. Prob. VIII p. 327
  7. ◇ Prop. XXXVII. Prob. IX p. 330
  8. ◇ Prop. XXXVIII. Theor. XXIX p. 332
  9. ◇ Lemma IV p. 337
  10. ◇ Prop. XXXIX. Theor. XXX p. 337
  11. ◇ Prop. XL. Prob. X p. 338
  12. ◇ Scholium Generale p. 339
Liber Secundus, Sect. VIII. De Motu per Fluida propagato. Book II, Section VIII pp. 354–373 annotation forthcoming
  1. ◇ Prop. XLI. Theor. XXXI p. 354
  2. ◇ Prop. XLII. Theor. XXXII p. 356
  3. ◇ Prop. XLIII. Theor. XXXIII p. 358
  4. ◇ Prop. XLIV. Theor. XXXIV p. 360
  5. ◇ Prop. XLV. Theor. XXXV p. 362
  6. ◇ Prop. XLVI. Prob. XI p. 362
  7. ◇ Prop. XLVII. Theor. XXXVI p. 363
  8. ◇ Prop. XLVIII. Theor. XXXVII p. 364
  9. ◇ Prop. XLIX. Prob. XII p. 367
  10. ◇ Prop. L. Prob. XIII p. 369
  11. ◇ Schol p. 369
Liber Secundus, Sect. IX. De motu Circulari Fluidorum. Book II, Section IX pp. 373–401 annotation forthcoming
  1. ◇ Hypothesis p. 373
  2. ◇ Prop. LI. Theor. XXXVIII p. 373
  3. ◇ Prop. LII. Theor. XXXIX p. 375
  4. ◇ Scholium p. 380
  5. ◇ Prop. LIII. Theor. XL p. 382
  6. ◇ Scholium p. 383

De Mundi Systemate, Liber TertiusBook III · The system of the world

Liber Tertius: Hypotheses Book III: the Hypotheses (later “Rules” and “Phenomena”) pp. 401–405 annotation forthcoming
Prop. I–XVIII Book III, Props. I–XVIII: universal gravitation pp. 405–422 annotation forthcoming
  1. ◇ Prop. I. Theor. I p. 405
  2. ◇ Prop. II. Theor. II p. 405
  3. ◇ Prop. III. Theor. III p. 405
  4. ◇ Prop. IV. Theor. IV p. 406
  5. ◇ Prop. V. Theor. V p. 407
  6. ◇ Prop. VI. Theor. VI p. 408
  7. ◇ Prop. VII. Theor. VII p. 411
  8. ◇ Prop. VIII. Theor. VIII p. 412
  9. ◇ Prop. IX. Theor. IX p. 416
  10. ◇ Prop. X. Theor. X p. 416
  11. ◇ Prop. XI. Theor. XI p. 417
  12. ◇ Prop. XII. Theor. XII p. 418
  13. ◇ Prop. XIII. Theor. XIII p. 419
  14. ◇ Prop. XIV. Theor. XIV p. 420
  15. ◇ Prop. XV. Theor. XV p. 420
  16. ◇ Prop. XVI. Prob. I p. 421
  17. ◇ Prop. XVII. Theor. XVI p. 421
  18. ◇ Prop. XVIII. Theor. XVII p. 421
Prop. XIX–XXIV Book III, Props. XIX–XXIV: figure of the Earth, precession, tides pp. 422–434 annotation forthcoming
  1. ◇ Prop. XIX. Prob. II p. 422
  2. ◇ Prop. XX. Prob. III p. 424
  3. ◇ Prop. XXI. Theor. XVIII p. 426
  4. ◇ Prop. XXII. Theor. XIX p. 427
  5. ◇ Prop. XXIII. Prob. IV p. 428
  6. ◇ Prop. XXIV. Theor. XX p. 429
Prop. XXV–XXXVIII Book III, Props. XXV–XXXVIII: the Moon and the sea pp. 434–470 annotation forthcoming
  1. ◇ Prop. XXV. Prob. V p. 434
  2. ◇ Prop. XXVI. Prob. VI p. 435
  3. ◇ Prop. XXVII. Prob. VII p. 438
  4. ◇ Prop. XXVIII. Prob. VIII p. 439
  5. ◇ Prop. XXIX. Prob. IX p. 442
  6. ◇ Prop. XXX. Prob. X p. 443
  7. ◇ Prop. XXXI. Prob. XI p. 448
  8. ◇ Prop. XXXII. Prob. XII p. 452
  9. ◇ Prop. XXXIII. Prob. XIII p. 455
  10. ◇ Prop. XXXIV. Prob. XIV p. 457
  11. ◇ Prop. XXXV. Prob. XV p. 460
  12. ◇ Scholium p. 462
  13. ◇ Prop. XXXVI. Prob. XVI p. 463
  14. ◇ Prop. XXXVII. Prob. XVII p. 464
  15. ◇ Prop. XXXVIII. Prob. XVIII p. 467
  16. ◇ Lemma I p. 467
  17. ◇ Lemma II p. 469
  18. ◇ Lemma III p. 469
Prop. XXXIX–XL Book III, Props. XXXIX–XL: precession and comets begin pp. 470–481 annotation forthcoming
  1. ◇ Prop. XXXIX. Prob. XIX p. 470
  2. ◇ Lemma IV p. 474
  3. ◇ Prop. XL. Theor. XXI p. 480
Lemmata V–XI, Prop. XLI–XLII Book III, Lemmas V–XI, Props. XLI–XLII: the comets pp. 481–510 annotation forthcoming
  1. ◇ Lemma V p. 481
  2. ◇ Lemma VI p. 483
  3. ◇ Lemma VII p. 484
  4. ◇ Lemma VIII p. 484
  5. ◇ Lemma IX p. 485
  6. ◇ Lemma X p. 485
  7. ◇ Lemma XI p. 486
  8. ◇ Prop. XLI. Prob. XX p. 487
  9. ◇ Exemplum p. 490
  10. ◇ Prop. XLII. Prob. XXI p. 509
Scholium Generale The General Scholium (added 1713; text of 1726) 3rd ed. pp. 526–530 annotated