[187] Newton’s Princ. philos. Lib. III. prop. 22, 23. [188] Newton. Princ. Lib. I. prop. 66. coroll. 7. [189] Menelai Sphaeric. Lib. I. prop. 10. [190] Vid. Newt. Princ. Lib. I. prop. 66. coroll. 10. [191] Vid. Newt. Princ. Lib. III prop. 30. p. 440. [192] Ibid. Lib. I. prop. 66. coroll. 10. [193] What this proportion is, may be known from Coroll. 2 prop. 44. Lib. I. Princ. philos. Newton. [194] Princ. Phil. Newt. Lib. I. prop. 45. Coroll. 1. [195] Pr. Phil. Newt. Lib. I. prop. 66. Coroll. 7. [196] See § 19 of this chapter. [197] Phil. Nat. Pr. Math Lib. I. prop. 66. cor. 8. [198] Ibid. Coroll. 8. [199] Ibid. [200] Ibid. [201] Newt. Princ. Lib. III. prop. 29. [202] Ibid. prop. 28. [203] Ibid. prop. 31. [204] Newt. Princ. pag. 459. [205] In Princ. philos. part. 3. § 41. [206] Chap. 1. § 11. [207] Newton. Princ. philos. Lib. III. Lemm. 4. pag. 478. [208] Princ. philos. Lib. III. prop. 40. [209] Book I. chap. 2. § 82. [210] Princ. philos. Lib. III. pag. 499, 500. [211] Ibid. pag. 500, and 520, &c. [212] Princ. Philos. Lib. III. prop. 40. [213] Ibid. prop. 41. [214] Ibid. pag. 522. [215] Ibid. prop. 42. [216] Newt. Princ. philos. edit. 2. p. 464, 465. [217] Ibid. edit. 3. p 501, 502. [218] Ibid. pag. 519. [219] Ibid. pag. 524. [220] Newt. Princ. philos. p. 525. [221] Ibid. [222] Ibid. pag. 508. [223] Ibid. [224] Ibid. pag. 484. [225] Ibid. pag. 482, 483. [226] Ibid. pag. 481. [227] Ibid. pag. 509. [228] See the fore-cited place. [229] Ibid. and Cartes. Princ. Phil. part. 3. § 134, &c. [230] Vid. Phil. Nat. princ. Math. p. 511. [231] Book I. Ch. 4. § 11. [232] Ch. 5. [233] All these arguments are laid down in Philos. Nat. Princ. Lib. III. from p. 509, to 517. [234] Philos. Nat. Princ. Lib. III. p. 515. [235] Ch. 5. [236] See Ch. 1. § 11. [237] Newt. Princ. Philos. pag. 525, 526. An account of all the stars of both these kinds, which have appeared within the last 150 years may be seen in the Philosophical transactions, vol. 29. numb. 346. [238] Newt. Princ. Philos. Nat. Lib. III. prop. 6. [239] Ch. 3. § 6. [240] Book I. Ch. 2. § 24. [241] Newt. Princ. Lib. III. prop. 6. [242] Ch. 3. § 6. [243] Newt. Princ. philos. Lib. III. prop. 7. cor. 1. [244] See Book I. Ch. 1. § 15. [245] Ibid. § 5, 6. [246] Chap. 2. § 8. [247] Newt. Princ. Lib. I. prop. 63. [248] § 8. [249] See Introd. § 23. [250] § 4, 5. [251] Newt. Princ. philos. Lib. I. prop. 74. [252] Ibid. coroll. 3. [253] Lib. I. Prop. 75. and Lib. III. prop. 8. [254] Lib. I. Prop. 76. [255] Ibid. cor. 5. [256] Vid. Lib. III. Prop. 7. coroll. 1 [257] Newt. Princ. Lib. III. prop. 8. coroll. 1. [258] Ibid. coroll. 2. [259] Book I. Ch. 4. § 2. [260] Newt. Princ. Lib. III. prop. 8. coroll. 3. [261] Ibid. coroll. 4. [262] Book I. Ch. 4. [263] Lib. II. prop. 20. cor. 2. [264] Chap. 4. § 17. [265] Ibid. [266] Vid. Newt. Princ. Lib. II. prop. 46. [267] Princ. philos. Lib. II. prop. 49. [268] Chap. 3. § 18.