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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. 396

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: 0.86.

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The machine reads it as

  1. ARTTAMELICA PFOPLXYI.
  2. P R OP: FXVI.
  3. Theorema.
  4. LCenica quancitale seriei alicujus inteerae, cognolcitur quanci-
  5. Tad Csce Oala.
  6. .
  7. C. F
  8. Duta, Si A B Friangutum sIC Z A B Paralleloprammi; et a6 Frianeulum, ab
  9. Parallelosrammi: cric reliduum Praperium, ZAB, 3 a 6. 17 Trem AB Parabola
  10. EHB Paralleloorammi cemeripei; de a P parabola Z a B parallelogramini circum-
  11. seripei: eric reliduum, E A B = 3 a B. Ex pariter in aliis. ti
  12. P R O P. LXVIF. oidi etriur 10
  13. Corollarium.
  14. Triangulum rectis quoclibet secetur basi parallelis e aequaliter ab in-
  15. virem remotis, (portiones aeque altas abscindentibus;) abseissa Trian-
  16. sula (verticem inter es rectas secantes,) sunt
  17. ut 2, 4, 9, 26, c. numeri quadratr. Sparia
  18. vero rectis illis interjecta, ut 27 3, 57 778c.
  19. Ariihmetice proportionales.
  20. Ouia Friangulorum abseittorum cam asticudi-
  21. nes quam bales sune Arithmerice proportionales:
  22. ergo plana in duplicata rarione Rrichmetice DrO-
  23. porcionalium, tire ue numeri quadrati, F, 4, 9, 16,
  24. ecc. FF Propterea, spacia incerjecta, 1, 3 A 2
  25. 5=(847= 16 - 9, eC.1
  26. EROP. FXVFTY
  27. Corollarium.
  28. Tconus planis quorlibet secetur basi parallelis, c aequaliter ab nuncem re-
  29. motis, portiones aeque altas abscindentibus;) abseisse coni (verticem in-
  30. ter C3 plana secantia) sunt ut L, 8, 27, 64 C5c. numeri cubici. Portiones
  31. vero interjectae, ut 2, 7, 29, 37, 80. disserentie numerorum cubicorum, (es si
  32. lc
  33. FIG. Pra
  34. ed.
  35. militer in Pgramide.)
  36. erir ratio conorum (qua ex alcicudinum e balium ralis) in ra-
  37. tione alcirudinum triplicata, sen ne X, 8, 27, 64, eec. EI proprerea portiones inter.
  38. jectae ut F, 7 = B = 1, 29 = 27 - 8, 37 = 04 27, e.
  39. Ouia cum conorum absciltorum alicudines sint Arichmetice proportionales, et
  40. propierea etiam balium diametri; adeoque vales in carundem ratione duplicata;
  41. PROF.

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. 396. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0416?run=74