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.
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.
[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.
[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.