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. 677

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: 0.84.

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The machine reads it as

  1. PrOP. VI. DeCalculo Centri Cravitatis.
  2. Complementum Parabolocidis Cubici, (proprer hujus Parabolocidis ordinatim.
  3. applicatas, in suberiplicaca ratione diametrorum interceptarum; adeoque ordina.
  4. rim. applicatas Complemenci, in Priplicara ratione diametrorum, sire dictanciarum
  5. a Vertice Complementi;) est Scries Ter-
  6. tianorum: Puta, ut OP, IP, 8P, 27P.
  7. Ec. Ulque ad P; adeoque summa omnium
  8. d
  9. 263
  10. de
  11. UC =N P; per F hujus; (hoc est, ad Pa OdP, +d p, 16d p, 8F dY
  12. ralleloorammum circumseriptum, ut F ad
  13. +:) Cum itaque Diltantixe CnE Ut Od,
  14. E d. 2 d 3 dus _c. ad. D: NIOmenta CrUNI
  15. ENDP = LNPxAD.
  16. UE Oap, E d p, 26ap, 8E ap, usque ad DP. FE Cimut omnia (per L hujuS) ut
  17. ENDP =ENPXSD. Et Diltancia Centri graricatis; ZD. Per 24 C aP. 4.
  18. Acque, ad candem formam, mutatis murandis, in aliis Paraboloeidium Com-
  19. plementis, aut etiam solidis eorum convertione circa Axem Tuum factis: aliitve
  20. lecundum ejusmodi alias series.
  21. Parabola, BAB, Fig. 127. (Propter ordinatim axplicatas in subduplicata ratione dia. L.
  22. metrorum:) est series Sublecundanorum; cujus Index Z: Duta, VOP, VEP, V2P,
  23. V3p, ecc. ulque ad P: Adeoque simul omnia, ut ZNP; (nempe ad Parallelo-
  24. grammum cireum (eriptum, Ut 2
  25. ad 3,) Der F hujus. FE PrOPteF
  26. diltancias, uc O d, 2 d, 2 d, 3 d.
  27. VOD, YEB, V2P
  28. Odqe
  29. Ed
  30. Sec. ulque ad D; NOmenL C. OdV p, 2 d V p, 2 a V 2P,
  31. TUnE, utOdVP, EaVFP, 2dV2D, dVoP, aVD, dvop,
  32. 3 dV 3P, ecc. vel ut a V Op
  33. aV FP, d V8p, d V 27 D, eC.
  34. ulque 2d DP: quae est, Peries
  35. ZNFDF = ZNPXZD
  36. Cuborum Sublccundanorum; cujus Index TZ vel 3. Adeoque (per F hujus)
  37. Omnia, UEZND P = ZNP XED. EE distantia Centri graritatis, 3D.
  38. Paraboloeides Cubieale, (proprex ordinarim applicatas in ratione diametrorum Cis
  39. Tuberiplicata,) est leries Subterrianorum; cujus Index z. Puta Ut V COP, V CP,
  40. V c2P, VC3P, _c. ad P
  41. E. L OMNIUI LUMMA, UEZNP;
  42. Der E hujus. (hoc clt, ad
  43. VcOB VCTP YCZB,
  44. Parallelosrammum circum. Od V cOP, Ld V Cp, 2 d Y C2P, 34Y C3)
  45. Seripeum, uc 3 2d 4.) Et,
  46. proprer distantias, uc Od,
  47. 2d, 2d, 34, etc. ad D: NO.
  48. menta erunt, ut, Od V COp,
  49. aY COp, aV CP, dVC+OP, aVCBEB,
  50. ZNDP= Z NPM3D.
  51. a
  52. DF.
  53. TdYCEp, 2aYC2P, 3dY C3P, eC ad DP; sire, ut dY Cop, a Y Cp, d Y C26p.
  54. qYCB+ p, ecc. ad DP; Series Biquadratorum subtertianorum; cujus Index F.
  55. vel Z. Ec Cumma omnium (per L hujus) ut ZNDP = E N PXZ D. Pc diltantia
  56. Ceneri gravitatis, ZD.
  57. Et similiter de aliis seriebus judicandum.
  58. Nempe, univertalicer; Si Index seriei Ponderum sit S; adeoque (per L hujus) HL.
  59. cumma corius, ue NP: Index seriei Momencorum, erie S. + L; adeoque
  60. norum summa, ut = = NDP. Ouxe per summam Ponderum NP di
  61. vita; exhibet = D, distantiam Centri pravicatis d verrice; nempe, ad distan.
  62. tiam maximam, ut S. f + ad 5 f 2: Adeoque reliquum distantia (quae est di-
  63. Pancia Cenuci oravicatis L Bati) ut g. D. EC propterea, Axio potrio ad Ver.
  64. ricem, ad porcionem ad Balem, ut 5 f 2 ad 1. Quod exat demonctrandum.
  65. Modque

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. 677. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0697?run=74