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. 312

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.

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

The machine reads it as

  1. DE SECTIONTBUS
  2. SP. PO. PB ::, hoc est.
  3. RrSO PO9 =
  4. VBKVSKNOC
  5. TAXAP
  6. XVA
  7. P0
  8. BSXAP
  9. 5
  10. ProD L
  11. continue proportionales.
  12. VBKYS = BS9. hOc elt, X09-
  13. B59
  14. VBKVS X V A X a r. e
  15. BSgKE= =VA. Ideoque proporrionalia BSq. VB, VS:: =
  16. VA.
  17. Elaberur eroo recta VA, adeoque Parabolae vertex A, in crure VB, unde ducta
  18. AP cruri VS parallela, est diameter Paratolae quaelica.
  19. Hoc est. Si Conus Propositus secetur plano per Avem, quod Basi Coni recrum
  20. sit trianeulum faciente VBS: e fiat, ut BSq quadratum basis trianeuli, ad
  21. VBKV S rectaneulum cruribus contentum; sic (quadratum ordinarim.
  22. sa
  23. applicatae in Parabola provosita, per Axem divitum, hoc est) Farus rectum Pa-
  24. rabolae propositae ai conveniens; ad VA distantiam vertieis Parabolae a vertice
  25. Trianculi, in utrovis ipsius crure mensurandam; t denique a vertice A recta
  26. ducatur AP opposito cruri parallela: eique Planum erisatur plano trianeuli VBS
  27. rectum: Planum hoc in supersieie Cori fasiet Parabolam, cui Parabola proposita
  28. coneruet.
  29. Demonstratio, per rexetica Anatoseos vellieia facile insiruetur.
  30. Pari tere methodo demonstrari poterit, Datam Fllipsin vel FErperbolam ( de
  31. quibus postea dicendum exit,) non quidem Cons cuilibet, sed sattem Conis quosli-
  32. bet specie differentibus, aptari posse. Cujus Propolitionis e Demonstrationem
  33. et Vecerminationem lubens praetereo, partim ne cadio Cim, nec velim cironibus
  34. ingenium suum exercendi antam praeripere, partim etiam quoniam illud insticuro
  35. noltro non est necestarium.
  36. P RO P. XII
  37. De Ellipsi sectione Coni facta.
  38. N ellipsi, Ouacrata ordinatum applicatarum aequalia sune differen-
  39. ciis binorum rectangulorum; quorum quidem illa (majora) sunt
  40. interceptis. Didmetris poporrionalia; haeC rerO (MinOTA) in CaruN.
  41. dem cacione duplicatd.
  42. Sunc enim Cuacrata DO aequalia Rectanoulis
  43. BDX DS, (peT PrOP. 7.) Ducta vero recta SFF,
  44. apsi A a parallela, e continuatis rectis BDS ad F;
  45. erunt ubique rectae DS = DF = PS. Et Rectan-
  46. suta BDX DS = BDKDF - BD X FS. SunE au-
  47. tem (proprer aquales rectas DF) Rectansula BDX DF,
  48. rectis BD provorcionalia, ideoque et rectis D A dia-
  49. metris intercepris (propier similia criangula ADB.)
  50. Rectansula vero BD X F S (quoniam tam BD quam
  51. FS rectae Tunt rectis D A proporcionales) Tunt in
  52. duplicata rarione diametrorum interceptarum D A.
  53. Cum ixicur lic ubique DO9 = (BDF DS =) BD
  54. XDF = BD XLS; constat propolic.
  55. P ROP. ZIV.
  56. De Clliptuco Lgramidoerde, e Converde, (seu Sphaeroeide) e Cuneo.
  57. (UE PrOP. 5, 6. Formarimus Prramidem vel Conum, _ PrOP. 9
  58. rim afracat I ellipsi Formetur Pyramidoeides ellipricum bieuspe
  59. (hoc
  60. Prramidocides Parabolicum,) ex omnibus quadratis DO ordina

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. 312. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0332?run=74