Leibniz Legible

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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. 793

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: 0.85.

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The machine reads it as

  1. PFOD. XIX. DeCalculo Centri Cravitatis
  2. Trem Omnes s, (corundem arcuum Sinus recti,) Tune iptum Frilineum rB0 F 1
  3. B R (per S 2. PrOP. 17.) ErSO Omn. = 25 R 2: = = ZB R 3.
  4. 269.
  5. irem Omnia Sh (ad bB F spectancia) 1B R, C peC BA. prOP. 18.) ELCO Omn. 270.
  6. aSBR: = = 8B= R 2.
  7. ErgO; Omn. Za R 2 - = 5 R = - = sB R: (hoc cAt, Ungulae bBF, aciem Ha-
  8. benes bB, momencum respectu ra; seu aciem habencis r a, momentum respectu
  9. DB;) 30. 2 R 2 - Z B R 3 = BB2 R 2 = 8a2 R 2 = B R3 f 35 2 R =; SCU (DTOPEEE
  10. a = 3 ∞ - a, _ B = 2 R = V,) =ER E P2 = 8a R = D + 3a R = 2 R a + V R
  11. =3s2R2
  12. Onod quidem, 3a2 R - 3 B R3 = 8b2 R= momentum, per Dnoulae BPr, aciem
  13. habencis bB, magnicudinem z a 2 R = B R (per SH. prOP. 17.) divitum; exti.
  14. bec ejuldem cencri graricaris dictantiam d ra, Z R -
  15. d FA, 3R + -
  16. + Sh= R2
  17. 402 -- 8B R: adeoque 2
  18. 4 a 2 - 8B p: ejusque relpectu T A momencum, da: R - 3b X
  19. Idemque Za 2 R = - 3 B R3 - d B R momentum, per Vngulae BBr, aciem ha-
  20. benuis ra, magnicudinem 3 a R2 - 3 5 R = = = sh R (per S L. prOP. 27.) divisum;
  21. exhibet hujus dictantiam centri graricacis a BB, ; c- f. 3 a. s R = aish - 6b t - 15. A
  22. a F57 + a - 3 as R + a SB - 6B R2 - B: R
  23. 6aR = 65 R = 25B
  24. 60R = 65R = 25B
  25. Adeoque ejusdem Ongula bBr (aciem habentis ra) momentum respectu F+.
  26. a2 X2 - 3 asR = a sB R + 3 b R = 3b2 R2. Idemque eAt, aciem tabentis
  27. Fr, momencum respectu ra
  28. Ouod quidem 3a= R = = 3 as R 2 - + a 5B R + 2 B R = 5h2 R 2 momencum.
  29. per Ongulae bBr, aciem habentis PY, magnicudinem, Za2R = a5 R + BR= (Per
  30. S H. prOP. 27.) dirisum; exhibet ejusdem Distancam Cencri gravicatis d 7 a
  31. R = 2e 5B
  32. 4 a 2 = 8a5 + 8B X; adeoque d F A, ZR -
  33. 2R +
  34. E = 2 a sB
  35. 442 - 8a5 = 8BR; ejuL.
  36. que respectu T A, momencum, 3a = X 2 - 3 a5 R 2 f ZB R 3 + a sB R = 3 B2 R2
  37. Idenque cHt, aciem habentis F A, momencum respectu F=
  38. Acque hOc demum 3a = R = = Z a 5 R 2- f ZB R 3 f + a s B R = SB= R2 WOMCH.
  39. cum, per Ungula bBr aciem habentis T A, magnicudinem, Z a R = -35 R? L Lsh R
  40. (PeT GF. PrOP. 17.) dirilum; exhibet ejuldem distanciam Cencri gravitaris d Yr,
  41. a-
  42. TOB R B R - 5a5R + ast
  43. TOR - 105R + 25b iadeoque, d bB, a 20B R - B R - 5asR + asto
  44. 10a R- 1OSR + 25h ejuF.
  45. ques relpectu bB, momencum, 3a2 R2 - 2b R3 + 5b. R2; idem quod aciem hy
  46. bentis bB, momentum respectu Y A, modo repertum.
  47. Ouaeque de Ingulis bBr tric dicta sunc; eadem omnino Ongulis ABR con-
  48. veniune; subltituris a pro a VprOB, T A prO Ta Aa Pro PT, d vice verta.
  49. Ouippe AbK porrio, limiliter adjacet rectis Y A, Ae, acque rb B rectis ar, 2I.
  50. Solidorum aurem, sire semisolidorum, respondencium magnicudo, ad maenicu.
  51. dinem Ongula correspondentis; eorumque momentum ad momencum hujus, (respe-
  52. au ejusdem plani ad convertionis axem aciemque Ongulae, recti;) elt ut X vel 38
  53. ad P. Distantiaque a planis ad conversionis axem, actemre Ongulae, rectis, uirO-
  54. bique eadem respectire.
  55. Dende
  56. : Si ex Ongularum ABBamomentis, SF tradiris; auterantur respectira
  57. Onculacum Bb Ba momenta: habencur respectira Momenca Ongularum ABB:
  58. e quae hinc dependene.
  59. Est aurem Ongula BbBa, aciem habentis b B vel Aa, (propter magnicudinem
  60. Ea= B, Der ST. PrOP. X7. Centrique gravitatis, in media longicudine Dolii, per
  61. PrOD. 2. distanciam a ra, Z B; adeoque d Y A, 2 R = ZB:) Momentum respectu
  62. ra, +a= B2; respectu PA, a B R = = a= B2: IIIudque : a 2 p2 (ob distantias et
  63. alicidines recipiocaras,) momentum etiam, aciem habenuis ra, relpectube vel
  64. Hhhhh

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. 793. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0813?run=74