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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. 338

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: 0.89.

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The machine reads it as

  1. DE SECTIONIBUS PFOPXXXIV
  2. Dueatur recta 2 A =F, e (in ejuscleni continuatione) AFI =d: REque ad
  3. rectam AII ponantur (ad OppOSitaS partes) duxe rectae inricem parallelae; AS =-1
  4. et HIB= a, (Talcem cancx line longitudinis AS, HB, ut AE ASXHB = Id :)
  5. Sicque anculus S AH = AH B quisibet acurus, (modo major sit complemento
  6. ansuli inclinationis in Flyperbola exposita.) Juncta rero aS producatur ut cum
  7. recta BFI producta cocat in S; e juncta B A producatur ut occurrat ipAi aS in
  8. V; ue compleacur erlareutum VBS; quod esto Friangulum. per axem in Cono
  9. construendo.
  10. Deinde super rectis AFI, BFLS, duo plana ita erizantur, ue comunis eorum
  11. sectio HIO, faciat ad rectam HB angulos rectos, ad rectam rero AHI angulum
  12. AFIO aequalem ansulo inclinationis in FIyperbola propolica.
  13. Hoc enim omnino tieri poste constac: Si enim recta quaelibet HO perpendi
  14. culariter intistens plano Frianguli V BS (adeoque angulos faciens vero (que OTHA,
  15. OTTB, rectos) circumrolratur circa rectam BHIS uc axem (invariato 2youlo
  16. OHLB,) donec ad licum plani perveniat in Hla, Faciacque in plano trianeuli angu-
  17. lum coFTA acutum, qui minor erie ansulo inclinationis in Hyperbola, (est enum
  18. ex constructione, angulus AHIB istius inclinationis complemento major;) ne-
  19. cesse est ut, in crantiu, aliquando fecerit angulum inclinationis angulo aequalem:
  20. (tactus enim cAt cransicus ab angulo recto, adeoque debiro majori, rel salrem aequali
  21. ad ansulum debito minorem;) adeoque cunc tuerit in sicu debiro ut sic duorum
  22. Planorum pront requiritur concurrentium communis sectio.
  23. In plano aurem BOS sic potico seribi intelligatur cireulus, diametrum habens
  24. BFS, qui sic balis cohi; aliique huic paralleli diamecros habentes BDS, conum
  25. complentes, (Per prOP. 5.) qui plano AHO sectus exhibebie Fyperbotat (Per
  26. PrOP. 7.) cujus ordinarim applicatx omnes (quarum TIO est una) ad diamecrum
  27. AHI angulum facient aequalem ansulo inclinacionis ordinarim apolicatarum in Ly.
  28. perbola, expolica act diameirum suam; sed e cisdemi sunc relpcctiro aequales (ut
  29. Parebit ex demonttratione prop. 17, et 20.) ideoque lingulae singulis consruunt
  30. adeoque e Fyperbola expolica Hyperbola sectione coni tactae. Ouod crat tacien-
  31. dum. Adeoque Hyperbola a nobis detinita eadem est cum ea quam detinic ApoI.
  32. Jonius. Ouod erar demonstrandum .t por e ts olto sil
  33. Sed de eadem opera doenimus Conum construere eique datam Fyperholam ila
  34. aptare, ut data ipsius diameter sit ciameter. ex reneratione: Aeque eciam Theore-
  35. matice verum elle LEuperbole diametrum. quamlibet fieri posse, in aliquo saltem
  36. ConO, Diametrum ex generatione.
  37. Fet 203 31t 5HIOC IsBIGB DEC.).
  38. 14 AS 1II
  39. sserloc st Cr rSCI
  40. oisitraaci n
  41. I ad eandem diametrum duxe FTyperbola OppOsito situ DOnan-
  42. tur, collutnem habentes diametrum cransvertam, idemque la-
  43. tus rectum; lintque ad il
  44. lam diametrum orcinatim.
  45. applicatae unius, ordinatim.
  46. applicatis alterius parallelxe:
  47. dicentur illa Lyperbolae-oppo-
  48. sitae; carumque rertices, can
  49. dem diametrum eranlverlam
  50. terminantes, Vertices Oppositi:
  51. Punctumque inter ODpoltOS
  52. vertices mecuum es utrique
  53. EIyperbolae centrum com-
  54. MunC.
  55. aurem Hyperbolae Opposi
  56. ix respondeno tly petbolis Oppo.
  57. sucorum conorum eodem plano le.
  58. atorum.
  59. eROP.
  60. mondous oi. - D R O DI IHXXIV. 2
  61. De Diametro transversa Fyperbolis oppositis.
  62. eresis c
  63. puci ) uert ogiel

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. 338. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0358?run=74