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. 334

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: 0.77.

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The machine reads it as

  1. DE SECTIONIBUS PFODXXXI.
  2. Item (propter Similia) EF. Ea:: DC. DO, hOc CA =, c:: Y d ~ +0c9
  3. 2dx = 0cq
  4. odx
  5. = DO9
  6. e =. D0. ejusque quadraum a N + 8 8 g + 207 d XC4e
  7. 8 ax - 8. 9 L 20y09 + 525
  8. a 42 X
  9. Tdeoque (urinque mulciplicando per s a de dividendo per e) y d2 N
  10. 02c 92 + 207 dx C9 = 5 d N = 8 d ∞g = 207 d x69 F dEd N C. Et (de-
  11. lendo utrinque = 207 d x C9, e transponendo) 02c 92 = 02 d X 92 = 8 d2 N
  12. =v a2 4= F SE a XC2. Ft (quia o - y = d E, Per 5 C 2) 0 ∞ 9 + 8 d N G
  13. = dEd N + dE d v c. Et (dixidendo urinque per d x + ~ = L f) o 9 = d E d X.
  14. hoc est 3E V = 9. Constat erBO PrOPOtitum.
  15. Illud Synihetice sic demonstratur, (rexeticis Analy seos veltixiis.) Ab F. IlipseoS
  16. CentrO C ducatur recta Ca, acque Esiplin in puncto a concingat recta a F, diu-
  17. metro cuilibet C A OccurrenS in F; ipsique parallela quaelibet OO rectae C a
  18. (intra Fllipsin) occurrens in c diametroque C A in CC; DIaMeITO aurem C A
  19. ordinarim applicetur a F, eique parallela Een _IAMEEIO OCCUrreNS in C. Fademque
  20. maneane Cymbola qua PriUIS e, d, L, 17 6787676,7.
  21. Sumantur aurem in diametro ucrinque a puncto c aequales rectae CD =, ,3 5 a X
  22. atque ordinatim. DONantuE DO, DO, rectae OO occurrentes in OO. Adeoque
  23. bisecantur tam DD in C (per conttruetionem) quam OO (propter paralle.
  24. la5) in E.
  25. Dieo rectam illam quamlibet OO (d recta Cia bisectam in 2) Estipsi in-
  26. teripcam ette; hoc est puncta OO este in perimetro. Quod sic probatur.
  27. Ouoniam sune (ut in Analy C demonstrarimus) P. F = --, eC = 7 4
  28. CA = d + = _ ea = 1 - =: Erit DC (= eG = CD) = 7 d +, plav
  29. =, eD2 = N - = pEd +
  30. 2
  31. e DA = d + = + 8E d
  32. Clanerulum DA = DA = = a v. + 8Z~ = 8E 5 ~ L 2 7CY dEd~. (nempe, pro q
  33. et q in amaluti; substiuendo YdEd C
  34. .) vel (quia 5 = 5E =y per
  35. SC2) eri D a , D 2 - 7 dr = dE8 L27CYSEdx
  36. dd
  37. Tum (propiee similia criangula) exit P. P. P. a:: DG. DO. hoc At, . c::
  38. rdx LOY DEdX rax LeY dEdE e = DO. ejusque quactatum Y d .
  39. odx :
  40. dEd ~C =2ra XCY dEd X -Y dx + 83C = 27CYSEdY 8 = DO9.
  41. 02
  42. a
  43. Sed es cancundem elt quadrarum Ordinatim applicata puncto D. Nam (pro.
  44. pter F. Hip(In) uE rectangulum P. A X F a ad rectangulum D A X D a; SIC (F ~G) qua-
  45. dracum Ordinarim applicatae in E, ad quadrarum ordinarim applicatae in puncto
  46. D. hoc CA a v. 2. d + 53C + 2 rCVdEdx Y dv +3EC = 27CYdEd
  47. d
  48. quod igitur est quadratum ordinarim applicatae puncto D, eltque (ue modo olten.
  49. tum clt) iptum DO9.
  50. 2

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. 334. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0354?run=74