Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[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. 546

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: 0.82.

Original at the GWLB · Page image · Annotations (IIIF) · Download text

The machine reads it as

  1. E C 1550LD L.
  2. Duod aurem omnes v = - hoc est, omnes L. Z. spacium L C. Z. AF complen.
  3. tes, ad omnes V: a D = a 2: Vel V aXV: D = a: hoc est, ad omnes I. K com
  4. plentes semicirculum, sne in ratione tripla; ex principiis Arithmeticae Infinitorum
  5. lic colligimus.
  6. Si series lublecundanorum sire Va, in seriem primanorum a invertum (hoc
  7. eltus in D = a) respectire ducatr, tiet Series DV a = aVa, Sive DY a -Y a
  8. quae cst ad seriem Aqualium lire tocidem D V D vel V D3, ut3 3 2d c, live
  9. uc 4 dd 25. (per PrOD. 64. et 73 Arithm. Infin.) Eodem modo l relpectire duca-
  10. tur eadem feries v a, in seriema = inverlam, hoc est in seriem Q: D = a: vel
  11. D2 = 2 a D + a2, tiet series D = V a = 2 D a V a a2 V a vel D= Y a = 2D Va
  12. F VaS, quxe est ad terrem A. qualium, Ere coridem D= V D vel VD3, ut 3-
  13. FZ ad F, live ut x6 ad 105. Fc limiliter, li eadem series Y a respectire ducatur
  14. in alias leries inversas, prodibume hae rationes Tubjecta. Nempe li teries V a duca
  15. tur inverte in
  16. Teries L. a. a. a. a. _c. prodibunt
  17. rationes =.
  18. 4
  19. 16
  20. 06
  21. 158
  22. 25 205 345 10305. c
  23. hoc est 2 2 X2 2Y2Y4 2 +2+476 2T2~4XOXB
  24. 3 325 3usXI 3H5N7H9 ZHGHMCOXTY dec.
  25. Si vero hi loci pro paribus habeantur, de suppleantur incerjecti loci impares;
  26. vonendo, in loco certio, (inter L et ay) pro Perie va in Va inverse ducta, ra-
  27. tionCM F ad ZD (PeF PFOB. 167. Arith. Insin.) Sieut racio loci quarti mulciplicat
  28. rationem secundi per Z, et hanc ratio sexii per 3, ecc. manisestum cst (ex Con.
  29. secutione fcriei) rationem quinci mulciplicare rationem certii per 3; e similiter
  30. in reliquis. Nempe series v a ducta inverle in 1
  31. Teries -,. 1. Va. a. V~. a. V a. ec. dabie
  32. a
  33. rationes L) =
  34. 242 2, 3 242 44 2 3
  35. 4 20 3 20 325 2G 6 3RsH7 2968
  36. ecc
  37. Onde, in praesens nesorium hoc laltem seligendum clt, series Va e Nad invi
  38. cem inrerse ductas, ad leriem aequalium, sire ad =V cocies sumptum, u
  39. x 3 ad 2; sive ut L ad 4∞.
  40. 21
  41. L: et3r. B s L~ GI. MB) LA
  42. Deinde, ue seriem Y a jam perpendimus, perpendamus similiier seriem ad
  43. Ea nempe ducta in seriem a inverlam, hoc clt, in D a dat Seriem D Va aYa
  44. vel D Ya = Ya cui convenit ratio 3 =3 ad 2, GVE 4 ad 35. PL similicer in re-
  45. liquis. Nempe series Va inverse ducta in
  46. sexies T. a.
  47. rationes 2. 4
  48. 5
  49. a
  50. 16
  51. ad 4 c. dabir
  52. 06
  53. 768
  54. 35 315 3465 45045
  55. _c.
  56. hoc est 2 242 2X2X4 2Y2N4H6 2X2XqV6 X8
  57. 5 SX7 SH7YO SXZKOKLL SXTXONLLKES. _C. (SCSI
  58. Si vero hi loci pro paribus habeantur, e suppleantur loci impares, ponendo
  59. (ver inquisicionem modo factam) loco certio (intex + et a) rarionem: VLra-
  60. iio loci quarri mulciplicat rationem secundi per Z; et illam ratio sexti per Z; HC
  61. rationem loci cerrii mulciplicabit ratio loci quinu per 8, ratio cerrii rationem pri-
  62. mi per S; es de reliquis similirer. Dempe leries va inrerse ducta in
  63. Teries . L. Vi. a. 1a a. Yu: l. aat
  64. sa
  65. ci
  66. 2244
  67. 25. L. 5. 13
  68. 4u 5 4l 517
  69. Al e 1050t 4l ot
  70. CaM

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. 546. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0566?run=74