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.
[98] Prop. 3; 8, 9; 13, 14.
[99] Prop. 4.
[100] Prælect. Geometr. pag. 123.
[101] Newton. Princ. Lib. II. prop. 10.
[102] Newton. Princ. Lib II. prop 10. in schol.
[103] Torricelli de motu gravium.
[104] Ch. 2 § 85, &c.
[105] Newt. Princ L. II. sect 6.
[106] L. II. sect. 4.
[107] See B. II. Ch 6. § 7. of this treatise.
[108] Lib. I. sect. 10.
[109] De la Pesanteur, pag. 169, and the following.
[110] Newton. Princ. L. II. prop 4. schol.
[111] See his Tract on the admirable rarifaction of the air.
[112] Book II. Ch. 6.
[113] Princ. philos. Lib. II. prop. 23.
[114] Book I. Ch. 2. § 30.
[115] Princ. philos. Lib. II. prop. 23, in schol.
[116] Princ. philos. Lib. II. prop. 33. coroll.
[117] Lib. II. Ch. 5.
[118] Ibid. Prop. 35. coroll. 2.
[119] Ibid. coroll. 3.
[120] Vid. ibid. coroll. 6.
[121] In § 2.
[122] Princ. philos. Lib. II. Prop. 35.
[123] Ibid.
[124] Id.
[125] h. 1. § 29.
[126] Princ. philos. Lib. II. Prop. 38, compared with coroll. 1 of prop. 35.
[127] L. II. Lem. 7. schol. pag. 341.
[128] Lib. II. Prop. 34.
[129] Lib. II. Lem. 7. p. 341.
[130] Schol. to Lem. 7.
[131] Prop. 34. schol.
[132] Ibid.
[133] Ibid.
[134] Book II. Ch. I. § 6.
[135] Vid. Newt. princ. in schol. to Lem. 7, of Lib. II. pag. 341.
[136] Sect. 17. of this chapter.
[137] See Princ. philos. Lib. II. prop. 34.
[138] Vid. Princ. philos. Lib. II. Lem. 5. p. 314.
[139] Lemm. 6.
[140] Ibid. 7.
[141] Newt. Princ. Lib. II. prop. 40, in schol.
[142] Lib. II. in schol. post prop. 31.
[143] Book I. ch. 2 § 82.
[144] Book I. Ch. 3 § 29.
[145] Ch. 3. of this present book.
[146] Ch. 4.
[147] In Princ. philos. part. 3.
[148] Philos. princ. mathem. Lib. II. prop. 2. & schol.
[149] Ibid. prop 53.
[150] Philos. princ. prop. 52. coroll. 4.
[151] Ibid.
[152] Coroll. 11.
[153] See ibid. schol. post prop. 53.
[154] Princ. philos. pag. 316, 317.
[155] Ch. I. § 7.
[156] Book I. Ch. 3.
[157] Book I. Ch. 3. § 29.
[158] Ibid. Ch. 2. § 30, 17.
[159] Book I. Ch. 3.
[160] Ch. 1. § 7.
[161] Chap. 5. § 8.
[162] Princ. pag. 60.
[163] Street, in Astron. Carolin.
[164] See Chap. 5. §9, &c.
[165] In the foregoing page.
[166] See Newton. Princ. Lib. III. prop. 13.
[167] Chap. 5. § 10.
[168] Princ. Lib. I. prop. 60.
[169] Book I, Chap. 2. § 80.
[170] Princ. philos. Lib. I. prop. 58. coroll. 3.
[171] Newt. Optics. pag. 378.
[172] Newton. Princ. Lib. III. prop. 1.
[173] Newton, Princ. Lib. III. pag. 390,391. compared with pag. 393.
[174] Book I. Ch. 3. § 29.
[175] Princ. philos. Lib. I. prop. 4.
[176] Ibid. coroll.
[177] Newt. Princ. philos. Lib. III. pag. 390.
[178] Newt. Princ. philos. Lib. III. pag. 391, 392.
[179] Book III. Ch. 4.
[180] Newt. Princ. philos. Lib. III. pag. 391.
[181] Ibid. pag. 392.
[182] See Book I. Ch. 2. § 60, 64.
[183] Book I. Ch. 2. § 17.
[184] See Ch. II. § 6.
[185] The second of the laws of motion laid down in Book I. Ch. 1.
[186] Newton. Princ. philos. Lib. III. prop. 6. pag. 401.
[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.
[269] Newt. Princ. philos. Lib. I. prop. 66. coroll. 18.
[270] § 8.
[271] Ch. 3. § 5.
[272] Ch. 3 § 17.
[273] Ibid.
[274] See below § 44.
[275] Newton Princ. Lib. III. prop. 19.
[276] Lib. III. prop. 19.
[277] Lib. I. prop. 73.
[278] Lib. III. prop. 20.
[279] Ibid.
[280] Opt. B. I. part. 2. prop. 1.
[281] Newt. Opt. B. 1. part 1. experim. 5.
[282] Ibid. prop. 4.
[283] Newt. Opt. B. 1. part 2. exper. 5.
[284] Ibid exper. 6.
[285] Newton Opt. B. I. prop. 10.
[286] Ibid exp. 9.
[287] Newt. Opt. B. I. part 1. exp 15.
[288] Philos. Transact. N. 88, p. 5099.
[289] Opt B. I. par. 2. exp. 14.
[290] Ibid. exp. 10.
[291] Opt. pag. 122.
[292] Opt. B. I. part 2. exp. 11.
[293] Ibid prop. 4, 6.
[294] Opt. pag. 51.
[295] Opt. Book II. prop. 8.
[296] Opt. Book II. par. 3. prop. 2.
[297] § 17.
[298] Opt. Book II. par. 3. prop. 4.
[299] Opt. Book II. pag. 241.
[300] Ibid. pag. 224.
[301] Ibid. Obs. 17. &c.
[302] Ibid. Obs. 10.
[303] Ibid. pag. 206.
[304] Obser. 21.
[305] Observ. 5. compared with Observ. 10
[306] Ibid. prop. 5.
[307] Observ. 7.
[308] Observ. 9.
[309] Ibid prop. 7.
[310] Opt. pag. 243.
[311] Newt. Opt. B. I. part. 1. prop. I.
[312] Opt. B. I. part. 1. prop. 2.
[313] Opt. B. I. part 1. Expec. 6.
[314] Opt. pag. 67, 68, &c.
[315] Ibid. B. 1. par. 2. prop. 3.
[316] Opt. B. II. par. 3. prop. 10.
[317] Opt. B. II. par. 3. prop. 15.
[318] Ibid. par. 1. observ. 7.
[319] Ibid. Observ. 19.
[320] Opt. B. II. par. 2. pag. 199. &c.
[321] Ibid. par. 4
[322] Ibid. part. 3. prop. 13.
[323] Ibid. prop. 17.
[324] Ibid. prop. 13.
[325] Opt. Qu. 18, &c.
[326] See Concl. S. 2.
[327] B. II. Ch. 1.
[328] Opt. B. III. Obs. 1.
[329] Ibid. Obs. 2.
[330] § 2.
[331] Philos. Trans. No. 378.
[332] § 11.
[333] Philos. Transact No. 375.
[334] Ibid.
[335] Opt. B. II. part 4.
[336] Ch. 3. § 14.
[337] Opt. B. II. part 4. obs. 13.
[338] Opt. pag. 255.
[339] Ch. 3. § 18.