FINIS. [Illustration] FOOTNOTES: [1] Philosoph. Nat. princ. math. L. iii. introduct. [2] Nov. Org. Scient. L. i. Aphorism. 9. [3] Nov. Org. L. i. Aph. 19. [4] Ibid. Aph. 25. [5] Aph. 30. Errores radicales & in prima digestione mentis ab excellentia functionum & remediorum sequentium non curantur. [6] Aph. 38. [7] Ibid. [8] Aph. 39. [9] Aph. 41. [10] Aph. 10, 24. [11] Aph. 45. [12] De Cartes Princ. Phil. Part. 3. §. 52. [13] Fermat, in Oper. pag. 156, &c. [14] Nov. Org. Aph. 46. [15] Aph. 50. [16] Ibid. [17] Aph 53. [18] Aph. 54. [19] Aph. 56. [20] Aph. 55. [21] Locke, On human understanding, B. iii. [22] Nov. Org. Aph. 59. [23] In the conclusion. [24] Nov. Org. L. i. Aph. 59. [25] Ibid. Aph. 60. [26] Ibid. Aph. 62. [27] Aph. 63. [28] Aph. 64. [29] Aph. 65. [30] See above, § 4, 5. [31] Nov. Org. L. i. Aph. 69. [32] Ibid. [33] Ibid. Aph. 109. [34] Book III. Chap. iv. [35] Book I. Chap. 2. § 14. [36] Ibid. § 85, &c. [37] See Book II. Ch. 3. § 3, 4. of this treatise. [38] See Book II. Ch. 3. of this treatise. [39] See Chap. 4. [40] At the end of his Optics. in Qu. 21. [41] See the same treatise, in Advertisement 2. [42] Nov. Org. Lib. i. Ax. 105. [43] Princip. philos. pag. 13, 14. [44] Princ. Philos. L. II. prop. 24. corol. 7. See also B. II. Ch. 5. § 3. of this treatise. [45] How this degree of elasticity is to be found by experiment, will be shewn below in § 74. [46] In oper. posthum de Motu corpor. ex percussion. prop. 9. [47] In the above-cited place. [48] In the place above-cited. [49] These experiments are described in § 73. [50] Book II. Chap. 5. [51] Chap. 1. § 25, 26, 27, compared with § 15, &c. [52] Book II. Chap. 5. § 3. [53] See Euclid’s Elements, Book XII. prop. 13. [54] Archimed. de æquipond. prop. 11. [55] Ibid. prop. 12. [56] Lucas Valerius De centr. gravit. solid. L. I. prop. 2. [57] Idem L. II. prop. 2. [58] § 25. [59] § 27. [60] Pag. 65, 68. [61] § 23. [62] § 20 [63] § 17. [64] § 27. [65] Hugen. Horolog. oscillat. pag. 141, 142. [66] See Hugen. Horolog. Oscillat. p. 142. [67] Princip. Philos. pag. 22. [68] Chap. 1. § 29. [69] Princip. Philos. pag. 25. [70] § 71. [71] See Method. Increment. prop. 25. [72] Lib. XI. Def. [73] Chap. 2. § 17. [74] See above Ch. 2. § 17. [75] From B II. Ch. 3. [76] Prin. Philos. pag. 7, &c. [77] See Newton, princip. philos. pag. 9. lin. 30. [78] Princip. Philos. pag. 10. [79] Renat. Des Cart. Princ. Philos. Part. II. § 25. [80] Ibid. § 30. [81] § 85, &c. [82] Princip. Philos. Lib. I. prop. 9. [83] § 92. [84] Ch. II. § 22. [85] Viz. L. I. prop. 30, 29, & 26. [86] Ch. II. § 21, 22. [87] viz. His doctrine of prime and ultimate ratios. [88] § 57 [89] § 3. [90] Ch. 2. § 22. [91] § 12. [92] Ch. 1. sect. 21, 22. [93] Elem. Book I. p. 37. [94] § 12. [95] Ch 1 § 24. [96] Ch 2 select. 17. [97] Newt. Princ. L. II. prop. 2; 5, 6, 7; 11, 12.