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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. 352

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: 0.81.

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The machine reads it as

  1. DE SECTTONEBUS PrOP.
  2. Erit isitur (propier Paraboloeides cubicale Bex PrOP. 45.) P A. DA:: P aC.
  3. DOc. hoc elt, d. d +5 Lg: : B3. s=2,5 =DOc.
  4. Irem (propter similia criangula) P. F. P a:: DC. DO. Hocest, 3d. P: : 3, d = 9.
  5. 3d
  6. 2p =DO. Ejusque cabus 27 ~ + 27 a 9 + dd9 = 4
  7. (ict 1 27 43
  8. =DOC
  9. 6=G
  10. Ergo (utrinque diridendo per pe, ee mulciplicando per 27 43) erit 27 d2 L2789
  11. FOdg2+93 = 2743 +27 d8 + 27 a29. RE (sublatis uerinque aequalibus)
  12. 9dg3=93 = 27 d8. Cujus quidem aequarionis radix q. si vel ope Coni lectionis
  13. vel alio quoris modo reveriri pocerit, monttrabit quaelita puncta D, D, (alierum
  14. quidem lupra punctum p. alterum intra;) adeoque propoliri vericatem. Incellise,
  15. t binae radticesque (Tursum et deortum Tumendae) tuerine inricem aequales.
  16. Analyli peracta, Demonstrationem Cynchericam sic liceret insticuere.
  17. In Parabolocide cubicali Aa diametro A P, Paralle la ducatuK a N: per cujus
  18. punctum quodvis (intra parabolocides) , ducatur recta r CF (diametro AP
  19. OccurrenS in G) Parallela tangenti a F (quae eidem diametro occurric in F. ) Frit
  20. an ejusdem Parabolocideos diameter, eique ordinatim polita n C.
  21. Diametro A P ordinatim applicetur a P, eique parallela ducatur r p (cidem dia.
  22. metro occurrens in p.) Fc lunco Cymbola P a = p. P A = d. FC = an
  23. Tum sumancur in diametro, utrinque a puncto p, aequales rectae pD == p D =9.
  24. utraque nempe tanta, quanca est radix hujus aequationis 9 d92 +93 = 27 d’ 8
  25. (Nempe Lbinae radices oppotiea, tuerine aequales.) Et punctis D, D, ordinatim
  26. ponantur rectae DO, DO, rectae in C occurrentes in O, O: qua cum parallela
  27. sint rectae x D, Licur recta DD (ex constructione) bisecatur in P, crit ideo O0
  28. (proprer parallelas) bisecta in n.
  29. Supereltixitur ut ollendatur rectam DO (bilectam in ~) Papabo loeidi interi-
  30. pram este, (’ut nempe ar recta bisecans sic diameter) hoc elt, puncta O, O, este in
  31. Parabolocideos curra; nempe rectas D O, DO, (diametro A P ordinacim PoHtaS,
  32. ex constructione,) ordinacim applicacis (ad eadem diameiri puncta) aequales elte,
  33. adleoque in curra terminari. Quod sic octendi polse videatur;
  34. DC = DC + pD = 3d +G
  35. 34
  36. ASIes
  37. Tum (propier Paraboloeides, cubicale) ut PA, ad DA; Sic cubus re-
  38. cta Pa puncto P ordinacim applicate, ad cubum ordinacim applicatae puncto D.
  39. hocest a. a + 8 =9:: P3. 8, Z p qui igimri cubus est ordinarim applicatae
  40. Duncto D.
  41. Sed et cancundem ett cubils tectae 150. Nam (propier Stilia crintibista ) PF
  42. 1.
  43. a SCLF AICI
  44. 3a L g
  45. Ysi
  46. Pa:: DC. DO. hoc est 34. p: : 3 d =9- 5 9 B =D O.; Ejulque crtous
  47. 27d
  48. 4 pS L. Vel (prO. 949 L93 substimendo
  49. erisit ~t
  50. Eha S, quae per construtionem tulne aqalius) 32 a1. L. 2s d. 9 L 22 d. e pr, vet
  51. l1337d21 8it
  52. 4+9 + 3 p = DOc. adeoque re
  53. denique (abbreviando tractionem, per 27 d 2d =
  54. Ex DO, DO, ordinatim applicarae sune punctis D, D, ad Patabolocieos curram
  55. terminatae in O, O: et proxierea recta O Paraboloeidi inseripta est ad diame.
  56. crum ax ordinacin. polita. Quod erat demonstrancum.
  57. Fac aurem disquisitio, quanquam prima tronte speciosa videatur; non tamen
  58. concludit: eo quod radix q ueriusque aequationis, lupponitur ejuldem magnicudi.
  59. nis; quod rerera non concingit, ut ex Aequationis Cubica Resolucione pacebie
  60. De qua plura diximus in Epiltola quae Fractatui meo conera Meibomir Dialorum
  61. Dratisiur.) Et propterea ejusmodi Parallela Diametri in Parabolocide Cubicali
  62. NOn REPCCIUNCT.
  63. EIISEC
  64. is
  65. AROP.
  66. esto aiie

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. 352. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0372?run=74