Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Ps. 1], fol. 296

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. 296
  2. F R A N CESCE d SCHOOTEN
  3. tionis ZZ = - aZ -- b b ∞0, guae per Z F vel - b ∞0 diridine.
  4. quic, per surdas quancicates exprimi portine: Suppono primum Z
  5. esse aqualis simplici alicui quanticari lurda, uEputa, V X, de fe
  6. Z = V x ∞0. Juam, ut ad aequationem quadratam ejuldem tor-
  7. ma perducam, in qua secundus terminus est rationalis, mulcipsi-
  8. care debeoper 2. L Y. L V x ∞ 0. Sed quonium (ic non producitur
  9. aequatio, in qua etiam tertius cerminus rationalis est, concludo
  10. radices aequationis propoliex hoc modo non porse denocarilive
  11. exprimi. Idem fit supponendo 2 ∞ -- V X.
  12. Ouocirca Catuendo nunc Z∞ y . L V ∞ Peu 2 - y - V X ∞0,
  13. oporcet iplam, ut ad aequationem quadratam ascendat, in qua rur-
  14. sus secundus terminus sic rationalis, mulciplicare per Z - p L V X
  15. ∞0, de ticZ2 = 2 yZ F y y ∞0. aequacio ejuldem forma cum al-
  16. lata, a in quaitem cerrius terminus rationalis est. Ilinc compa-
  17. rando secundum terminum unius cum secundo alcerius invenio
  18. =27 ∞ - a hoc eA, y ∞ =a. Tertius autem terminus cum tertio
  19. comparatus dat yy = x ∞ -- bb. In qua li in locum yy subroge
  20. tur = aa, habebo = a a + b b ∞ X. Ac proinde cum pro quaesiris
  21. radicibus suppoluerimus Z ∞0 y. L V X, X Z ∞ y - V x, eruncipla
  22. 2 ∞ = 4 + V = aa = bb, e 2 ∞ : a - V = a a + bb.
  23. Eodem modo si inrestigare relimus, quo pactoradices aequa
  24. tionis indirilibilis py L a p -- b b ∞0 per quantitates Curdas ex-
  25. primi queane, Cacuatur (neglect â suppolitione iplius y ∞ 8 V ∞)
  26. p∞ - 2 Y V X (Cu Y. L Z - V X DO, Caque, ut ad aequationem
  27. quadracam altursac, in qua rursus se cundus terminus lic rarionalis,
  28. mulciplicetur per y + 2 f V ∞ ∞ O, _ tt y y L 22 7. + ZZ ∞O.
  29. X
  30. aequatio ejusdem Formae cum allata, ee in qua etiam tertiuscermi.
  31. nus est racionalis. Unde comparando secundum terminum hujus
  32. cum secundo illius inrenitur Z ∞ 3 a. Perrius autem terminus
  33. cum tertio comparatus dat x ∞ = a a -L bb. Atque adeo, cum pro
  34. quaeliris radicibus suxpoluerimus y ∞ = 2 F V X, eC y ∞ = 2
  35. =V X, erunc ip (X : y ∞ = 2 a + V : a a F bb, _c y ∞ - : a -
  36. +aa L bb.
  37. Similiter, inveltixando num radices xequationis Z 2 - 4 Z f bb
  38. ∞0, quam per 2. F rel - b ∞o diridere non licet, per lurdas
  39. Quan.

Cite

[Ps. 1], fol. 296. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175905688X:0318?run=74