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[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 889

Machine transcription. Not an edition. Errors are expected: about 8% character error rate on Latin and French lines, higher on German. Mean line confidence on this page: 0.81.

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The machine reads it as

  1. Ouo itaque habeantur Omnia a 3 V; HoCCll, Omnes _, (seu BV recta Figuram
  2. _ vEV7, _C. ComplentES) respectiris a (serie Pertianorum) onulta: Incellisa
  3. mus, juxra doctrinam prop. 10. hujus, (quam Cepius in auxilium adrocarimus,
  4. Singulas an B, 7, ecc. H15. 135. aequaliter ab invicem remotas, coridem elle respectiras FiB. 135
  5. x rectas; adeoque ipsam AF onustam, scu Omnia, a + B F 7 _c. = Omp. x
  6. =5 R, ut jam oltentum est, Cx S B. pFOP. 17.
  7. Florumque omnium momenta respectu axis A; hoc CH, Omn: a N; TUNE ipL
  8. onustae rectae, AF f BF F CF, ecc. hoc elt, roridem A H, dempris omnitus A B
  9. = AC, _c. HTOC CH, (PrOPrer A F = s R,) cocidem sR ultimis (Teu a sR,
  10. dempris omnibus sR anrccedentibus, pro arcubus arichimerice proporcionalibus
  11. V(que ad a ulcimum.
  12. Sunc aucem (pro aceubusa arichmecice proporcionalibus) omn s, =u R, per
  13. 8O. PrOP. X7. (utpotC ipsa aBV F3. 270.) Adeoque Omn. SR, = V R3. HOC
  14. itaque ex as R subducto, habetur a S.R = V R2 = Omn: a v.
  15. 1L
  16. Incelligantur deinde eadem an B, 7, _c. Hx. 135. tanquam cocidem aN: adeoque
  17. onuctq recta AB. =Omn. a N, = aS R- V R 2. PTorumque omnium momenta re
  18. spectu iplius A; hoc est Omn. a = N; Func ip (a AF f BF. F CF, Sc. rectae sC
  19. onusta. Hloc est, rocidem AF, (= a7S R aV RZ,) dempris Omnihus AB F
  20. AC, Ccc. hoc et, omnibus asR = 2 R?, pro arcubus a arithmetiee proporciona.
  21. Libus.) 3.5p0
  22. Sunt autem (pro arenbus a arichmetice proportionalibus) Omn. a5, = - e R 2
  23. + av _ per SO. PrOP. 27. Curpore momentum ipsius aB.fg. 270. respeCt 1C
  24. ctae Aa;) adeoque Omn. asR, = - e R3 = a V R2.
  25. Tiem Omn. V, = e R, per SB. prop. L7. (uipore iptut A B R crilineum, 1.8.
  26. 270.) adeoque Omn. - v R
  27. ErGO, Omn. a s R = v R2: = - 2C R3 + av R - - 2 a R3 + 25R + avse
  28. HIoc itaque, ex a SR = a V R, Tubducto; habetuE Z a R 3 25 R 1 2aV R
  29. a25R = Omn. a2 X.
  30. Incellisaneur denique eadem a, B, 7, dec. fig. +35. Catigliam coridem a: allloque
  31. onulta recta AH, =Omn. a 2 ∞, = 2 a R3 = 25 R =, 2a V R 2 + a 2 5 R. IIO
  32. rum itagiie omnium momenta respectu axis A, hocCsL, Omn. a X; TunC iI A P.
  33. = BF. F CF, Sc. SCOnultX: FTOC CHL, coridem AF, (= 24Z R3, = 2as R3 -
  34. 2 a 2 V R + as R,) dempris A B f A C, dec. TTOC elt, omnibus, 2 a R 3 = 25R3
  35. 2aV R 2. a = s X, pro arcubus a arichmetice provorrionatibus. P2 13g 15. 11
  36. Sune aucem (pro. a arichmetice provorrionalibus) Omn. an FF ZaV, DEN DEOP. 5.
  37. hujus. Adeoque Omn. 2. a 13, == a Z R3.) essd 5 esistosieB esdso elisiin e
  38. Tiem, Omn. S, = v R, Per SO. prOP. 17. adeoque Omn: , 2. SR3 =2 1(2 ∞ R
  39. mtrem, Omn. a v, = 3 a = R -- a 5 R = V R~, Per SFI. prOP. E7. (uipore momen-
  40. cum cilinei AbK. HB. 1 70. respectu Aai) adeoque Omm. = 2 av R2, = = a R.
  41. 245R3 = 2V R2.
  42. Trem, Omn. a2 s, = = a R2 + 2 a s R + a e v R 2. y R2, per S, O. BFOP. 19.
  43. (nempe Onculae a Bv fz. 270. aciem habentis Aa, monrentum relpectu Aa;
  44. Adeoque Omn. a2S.R, = a R3 = 2a5 R3 + a 2 V RZ - 2V Ra01 +S
  45. FFO, Chorum neprepatum) Omn. 2. a R - 2. s R2 = 2aV R, + aZ sR, =
  46. 4a5 R3 F a dk 2 - 6V R
  47. Hoc iraque subducto, ex 227 R 3 = 2a5. R3 = 2a 2 v R + a sR; habetur,
  48. 6vR + 3a R3 = 6aSR3 - 3a v R = = a sR, = Omn. a N
  49. Arque ad eandem Formam, (eadem quoties opus erit repetendo restigia) proce
  50. dendum esset, E POrro Omnia a +, Omnia a3X, (aut etiam ulera) inquirenda el.
  51. sent: Vel etiam, Si loco iplorum x, alia quaelibet quantitates ponerentur, Ouod
  52. nic obicex n etLB. 193. CssAE cALB
  53. Clsa ntaque ( uc jam anee ostensum eAt S P.) singulorum Sectorum exiguorum MaB: Fix. 193.
  54. nicudimes, timc t 11. Z
  55. 28
  56. a RL
  57. 22
  58. ;distanciaeqi, ab P NC, R X =
  59. vuunu
  60. e
  61. a X
  62. 383 (Po. 200.
  63. Fto
  64. PFOP. XXVII. DeCalculo Centri Cravitatis.

Cite

[Johannis Wallis S. T. D. Geometriae Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica] Johannis Wallis S. T. D. Geometriæ Professoris Saviliani, in Celeberrima Academia Oxoniensi; Opera Mathematica, fol. 889. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0909?run=74