Leibniz Legible

Machine transcription of the Leibniz Nachlass

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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. 774

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: 0.83.

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The machine reads it as

  1. De Calculo Centri Cravitatis.
  2. CapV.
  3. Aa erectis 8R3 P + Ze R3 = av R2 F 4 5VR= = 3 a S2 R. REGUE HXC MOMenLA per
  4. Magnicudinem dirila; extribene solidi bB2 diltanciam Centri gravitacis a plano
  5. Aram =
  6. P - 6CR - 65VR- 45
  7. oleic 48 R2 = 24 V R = +25
  8. i a planO TCN
  9. R 4V R - 4s R F s2V
  10. 12 R - 60R - 35
  11. ab Aa Plano, 3 + 10CR2 - 8av R + 25V R - 4a5
  12. 16R = - 8V R - 4.
  13. Similitet, eum solidi porcio AKBa paralletogrammo incumbens, Magnicudi-
  14. nem habeat ( ex ductu A a = 2 R, in a B0 = V R, Factam,) 2V R2; et Momen-
  15. rum respectu plani A Ta crecti, (ex ductu Magnicudinis 2v R3 in distanciam
  16. Cencri pravicaiis plani a. BV, a r0
  17. R
  18. (D per 6 O, O. prOP. 17.) ZC R.
  19. =5VR2; _ respectu ran crecti plani, (ex ductu a C = R, dimidii longitudi-
  20. nis pritmatis, in magnicudinem 2V R2,) 2V R3; de respectu Aa crecti plani, (Cx
  21. ductu magnicudinis 2V RZ, in distanciam Ccurri graricatis plani a B0 ab A a, HOC
  22. ost, in
  23. eR + aD
  24. 3 Der SP, C. PrOP. 17.) = 2 eR F 2 av R (est enim
  25. Prismaris centrum gravicatis in medio recta Cencra gravitatis batium oppotitarum
  26. jungente, Per PrOP. T, _ 5 hujus:) Si ex his Solidi A K Ba magnicudine e mo-
  27. mentis; auterantur Magnitudo ee Momena respectira Solidi A DBa; V R3 F Z5 R
  28. et 3CR3 + 250R +553R; e ZV R = Z52 R2 = 3S VR; _ = ZC R. aV R
  29. =ESVR Za S R: Tupra cradtiia: Relinquentur, Solidi ABK, magnitmdo, (hoc
  30. est, ascresatum Omnium su, co spectancium, sumpris a arichmerice proporriona-
  31. Libus,) VR = =s R = ZVR; Momencum respectu plani A ra crecti, (hoc elt.
  32. Omn. = s, co spectancia,) iCRF 45V R ==5R; Momentum respectu plani
  33. ran erecti, ZV R = 3s2 R2 F Z S VR = 3 V R + SSVR; Momentum respectu
  34. plani Aa, (hoc est, Omnia a 5V, eo spectantia,) =ZC R F aVR L L SVR
  35. =Za SR. Atque haec momenta, per magnicudinem dirisa; exhibent, Solidi
  36. ABK, ditanciam Ceniri graricatis d plano A+ a, 3e R F 3SVR = 253
  37. plano 2an, 160R = 8 s R. + 2 52
  38. 12VR - 65 =68
  39. L3R +.
  40. 12VR - 65 =6v
  41. =B2
  42. 32
  43. i (adeoque, d Y A, 3 R -
  44. 30 3R + 3 h == ZV; et propiorea ejusdem respectu T A, momencum, hoc est
  45. aegregatum Omnium ; 5~, eo spectancium, sumpris a arichmerice proporionali.
  46. busu 523 R = Z~= R~ = ESEDR = ZVR = 3 sR =5SVR;) distanciamque ab
  47. Aa plano, =3C R + 4 a0 R + 5V R = 2 a 5
  48. +VR = 25 = 28
  49. Trem; Portionis A L bB, magnimdo ee momenta, habencur ex Porrionum AB F,
  50. es Ab B, magnicudinibus et momentis (respectire) additis: Vet subductis Por-
  51. tionis b B0. B magnitudine ee momentis, ex magnicudine e momencis (respectiris)
  52. porcionis AKBa: Vel etiam eodem modo quo habentur iptius bBa B magnuudo
  53. _ momenta. Nempe ex ductu plani a B0 = ~ R, in AY = 2, habetur iptius
  54. AR BB (pritmatis) magnirudo v R. Acque ex hac magnicudine in 5~ (ejuI.
  55. dem CentTI BTAVITALS a P A rel b B distancam,) habetur ejuldem, respectu P A
  56. vel bB, momentum, 5 v R. Duetaque in B = : v = 2 R = 3 v (dillantiam a
  57. ay) ejuldem momencum respectu + an 2v R = E V R. Fademque magnicudine
  58. ducta in Ceneri pravicatis distantiam ab Aa, = C R + a~; et d plano Ar an
  59. CR. = 50 Cealdem nique quae sunes in a bo plano, distantia ab A C, d ra; )
  60. habencur ejuldem momenia, respectu A a, a V R = c. v R2; e respectu plani A r a,
  61. evR2 = = 5VR.
  62. EE cinilicer de porcionibus alio, mucacis mucandis, sudicandum eric.
  63. Supex ADa Semicirculo, crigi incelligatur Cylindri recti porrio; ea ratione,
  64. ue super singulas B V ordinacim applicacas, alticudinem habeat respectivis b B
  65. qualem,
  66. 1C

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. 774. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0794?run=74