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Leibniz-Handschriften zur Mathematik LH 35, 6, 1, fol. 8r

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: 0.95.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 9v); this page is its right half.

The machine reads it as

  1. si paraboloeides sesquialteri gradus AB, cujus a,
  2. tangens vertois AD, vertex A, tangens verticis AD, evolvatur
  3. ad juncta ad filum recta AE, quae sit 8.24 lateris recti parabolocidis
  4. discribetur Parabola EF, cujus latus rectum erit bis EA, unis EAD, et
  5. ad eam normalis BG BGF, (aequalis AB+ EA BA + AE) tangens curvam
  6. AB in B, secans axem in G, erit _ Ex puncto F in rxem agatur ordinata
  7. FK, fiet RG = AE, adeoque EK = AG
  8. similiter evolvatur
  9. alia (A (B) Colet moda pescta, indefinitesime differens a priore
  10. et punctum intersectionis sit Y, ex quo in axemagatur YX
  11. Ad, Z ED, V latus rectum b. fit 2 = hvo EA, ek: 27, ser KG EK, 9 KF, c, et
  12. (1)
  13. fiet aco = 1bh. 279 sit CE = AC e CK = EK + CE = q+ e Y et ex aeq. 2. per 3 fit
  14. C0co= 16: 27 et tr-he. quaeritur punctum intersectionis, Quod fieri potest, differentiando
  15. aequationem 4, ita tamen ut a sint contanter et Y sint invariatae in differentiando, h et e, variabi
  16. et fiet rdh - nde- Pdh = 0 oportem autem relationem aliquam sumi inter e et h, ea
  17. enim arbitraria est, ponamus verb. g. e = h seu CE = EA, fiet de =dh ergo ex 5g. 5. firt
  18. in cosa parso Y = 2h = 2C seu in casu concursus Y, fore CX = bis CE = CA, seu coincidere X et A.
  19. et quia in casu concursus est r = X et c0 = y ergo ex Z et 8 fit h = X: 2 ergo ex aeg. 4. per 9et 10
  20. fiet: gy = 1b:27 XX: 2 - XX: 4 seu yy = 4: 27 XX seu y = 213X: B3 locqus ergo omnium
  21. intersectionum est recta CY, quae omnes parabolas tanget, quod et ex eo patit quod

Cite

Leibniz-Handschriften zur Mathematik LH 35, 6, 1, fol. 8r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 39). https://leibnizlegible.com/page/00067956:0015?run=39