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. 419

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: 0.80.

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

The machine reads it as

  1. erOP. CXXV.
  2. IHEENLTORUM.
  3. dictis ad PFOP. I2F. _ 723. NTam
  4. segmenta recta BB in hac Figurs
  5. Demonctracio facile patet ex
  6. tancundem ralent aeque scomen-
  7. ea BlaMLELA ASuTa. 5C1
  8. Ent aequales, quam recta AD, DF
  9. circuli sive Ellipseos AH, ma-
  10. jor ett auc minor quam Ouadrans, Prout DB major cst aut minor quam DB.
  11. Si autem tam rectae AD, DF
  12. ad invicem verpendiculares, CrunE
  13. ip(A DE, D L, ordinacim axpli
  14. cata in circulo; sn mins, Cal-
  15. tem in ENtipH. Portio autem sve
  16. P ROP. CXXV.
  17. Theorema.
  18. L exponatur series Aqualium mulctata serie Ferrianorum; Re-
  19. Siduorum Ouadrata, Cubi, Biquactrata, ec. ad seriem tointem
  20. eorum maximo aequalium, rationem habebunt cognitam. . sel eup
  21. _C. del
  22. -
  23. Nempe,
  24. Cabi.
  25. R =00R5. [00R -00
  26. R = 3 a 5 = 3 a R - a
  27. R = 3B R5 f 335R3 - 321P 1
  28. A - 303 R f 3 c R3- C2, 108
  29. ec. ulque ad
  30. RE= 3 R3 R F 3 R R3 - R
  31. summa A R = = A R) AR = Z AR. F ; ARAR = Z A R F 3 A R = AB
  32. nemDe L
  33. vel
  34. 3X 6, ic 23 113 sisC 3 X6IX, 91101F 9O1l cst, pIL
  35. ausq..B V solve eot Cq Xuy usd ualBB X 3X XO River 111 101
  36. EL BC deinceps, continue mulciplicando numeros drichmetice proporionales
  37. (quousque cujustibet porestaris gractus poltulat) a 3 et 4 ternario concinue
  38. creleenies. ioin sae i
  39. sr cunitamm omirum P, R O P. OXXVL. 0 mbilest eodinoisilia
  40. Theorema.
  41. Ari modoq Si exponatul series Aqualium muletata terie Cilarta-
  42. norum, Ouintanorum, Sextanorum, etc. Residuorum Ouadra-
  43. ta Cubi Biquadrata etc. ad seriem toridem eorum maximo aequa-
  44. lium, rationem habebune GoeniTam. B
  45. e ic ads sidccteuer siestrit
  46. aste
  47. ei Iui iBOcritr
  48. Puca 1 - 5 = 3. 2 = 3) 5 =, 13. B = 3 + 3. pih = 5B. it p hct 13 13. F. ii == 32B.
  49. vet
  50. 4X8-
  51. 5X9
  52. 4.XB X 1Z, cu∞hs guci b d 4 X BX X2 xh6. visil
  53. 5XOX13
  54. SXOXF3XL7
  55. TIem L - 8 = 3. F - 3 + ,i = 85. 1 - 3. + 52 = 16 = 18 8. F- 8. f 5 - 18 + 1i = 1r0
  56. vel
  57. 5XTO
  58. 6x2F
  59. SXTOXF5
  60. 6XIFX16
  61. 5XLOX F5 X20
  62. 6XTZXT6XZF
  63. Ec sic in aliis quibusibet; nempe continue mulciplicando numeros Arichmetice
  64. proportionales (quousque gradus pottulat) a 4 e 5, vel 5 _ 6, vel 6 _ 7 ec.
  65. quaternario, vel quinario, vel lenario, _c. (secundum indicem seriei subductae)
  66. contmue crescentes. Prout inductione parebic. Ad huncmodum,
  67. (8S 2
  68. Seriei
  69. Serdei
  70. R3-
  71. Oiacrata
  72. D6-
  73. 26
  74. 25
  75. 2
  76. 00 R3 OC
  77. 2. a
  78. 2b3 F L L
  79. ec. ulque ad
  80. Ro = 2R3R3 FL

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. 419. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0439?run=74