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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. 351

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.

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

The machine reads it as

  1. PFOp. XI. VI
  2. HLC L S
  3. e RO P. XL V1.
  4. De recta Paraboloeides Cubicale contingente.
  5. F Paraboloeides Cubicale A aq in puncto quoris an contineat re-
  6. eta _ F, diametro P A OCCuTTenS in F, Stque cidem diametro
  7. Ordinatim axplicata a P: erit recta A F (diamerri Continatio) du-
  8. pla diaHCCI InTExCePIA P A: hOC ett, diameter continuata P F, tri-
  9. bla diamerri P A.
  10. pram, sumpeo ubivis (in eadtem diametro) vupeto D, cui ordinatim abplice.
  11. tur DO, tangenci a F Occurrens in P: Punctum Y (prOpter tangenTEM) vel CxIE
  12. idem cum puncto a (E nempe P, D, coincidanE; ) rel (si secuS) exit L exta
  13. curram: e (prOPterCa) DF = DO (nempe aequales, si D, P, coincidant; rel
  14. A secuS, D T lonsior erit.)
  15. Ponamus autem (ob. commodiorem calculum) P a = p, P A = d, PF = f,
  16. PD = a. Eric ergo (per det. praeccd.) PA. DA:: PaC. DOC. hoc est d. d = a
  17. : P
  18. P =DOC. liem (propiex similia criangula) PF. Pa:: DF. DF.
  19. hoc cA f. P.: 5 = a. p = D T. Ejulque cubus
  20. DTC) = (DOC =
  21. a
  22. 23s a +3sa La
  23. P. Fr (urinque multiplicando per fod, et divi
  24. dendo per p3) erit f3 d = 3 f d a 3fd a2 = da f. d =f a. Tum C alite
  25. rendo utrinque f d, ec dividendo per L a d erit 3f L = 35 da + d a =f. De
  26. nique, porendo puncta PD coincidere, (ut craneleat quancilas an adeoque et ips-
  27. uo mulciplicia = 3F dan = d a 3) eric 3f d = f, hoc elt. 3a = f. Quod erot
  28. demonstrandum.
  29. F R OP. XLVII.
  30. De Parabolocidis Cubicalis Diametris.
  31. Nquirere, An in Paraboloeide Cubicali Diametri sine invicem pa
  32. rallela: Er cujulris diametri Ordinatim applicata, sint rectae in
  33. ipsus Vectiee conringenti parallotae.
  34. Inquilucio sacile instimi pocerte ad imicacionem illius quae de Parabola achibe.
  35. tur ad prop. 24. nili quod PF, quae iltic dicitur 2 a, hic dicenda est 3 d. Fam
  36. nempe Anatycice sic inllicuamus. Supponamus scilicet rem ita este: Adeoque re-
  37. etam l’a, quae paraboloeides Aa in puncto a continsat, diameno P’A producta
  38. OcCuTrerE in F; eique parallelam OO Paraboloeidi inscriptam, quae (producta)
  39. cidem diaerro supra verticem occurrat in C) (adeoque intra verricem diaetro
  40. Occurrat, cum tam. duarum D Ei, quam duarum DO, de quibus mox dicetur, al.
  41. Eera eriu quantitas negatira, quod tamen calculum non curbabit; ) iplanique 00
  42. rec
  43. ipsi a ordinacim axplicata;) denique diametro AP ordinaciim applicari OD,
  44. ODa P iplique Paralselam r P eidem diametro occurrere in P: quare e (prOPIeI
  45. Paralletas) Pp = a 2 = F G; _ ProPterCa P F = P C: item (propter parallelas)
  46. rectam DD. bilectam in p, SeutO bisecatur in 2. Ouarendum autem est, num-
  47. cubi reperiri poltine puncta D, D; quae, quidem licubi inveniantur, conslabir pro.
  48. Dolutum.
  49. Sublticuris igitur idoneis lymboto = P. P A = d. (ideoguC, D Pa-
  50. ced: PF = p G = 3 a.) PP = a n = F C = 8. (erBO p A = P A F Pp = 4 + 8.
  51. PD = g. (adeoque D A = p A L pD = d + 5 Lg. _DC = p C + pD = 3d =9.
  52. Fxit

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. 351. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/851387705:0371?run=74