Leibniz Legible

Machine transcription of the Leibniz Nachlass

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LBr. 57, 2 · Bernoulli, Joh., fol. 76v

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: 0.92.

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. 77r); this page is its left half.

The machine reads it as

  1. OB. DB::dG. GE et OB in G2 = DB in DG, et sumendo utii
  2. uigue duplum AB in GE = DB in AC plus DB in AC, addeado
  3. utriques AB in AG vel CD, erit AB in AE = DBin AC plus
  4. DB in AC plus AB inCD, est autem lem. 1. DB in AC plus
  5. AB in CD aequale BC in Ad, ergo AB in AE = DB in AC
  6. plus BC in AD. Q. E. D.
  7. Demonctratio fornulae sectionis anqularis,
  8. firce pramissir, res ita peragtur: Eito dianeter AB = 1
  9. subterta AC = X, adeoque BC = Si- xX = (brevitalis gr.
  10. y subteasa AE = a, adeoqe BE = Vi-aa (breo. gr.
  11. Ponantur primo arcus AC, DE contigui, evarescente
  12. intermedio CD, ita ut arcus AE sit duplus ippus AC;
  13. quo casu verta AD, AC ut et BD, BC coincidunt, adeoque
  14. per temma 2. erit yy - XX = b. et per bm. 3.. 277 = a;
  15. ponatur nunc arcus iatermeduis CD aequalis ipsi AC vel
  16. CD, ita ut arcus AE sit triplus arcus AC: ergo per praced
  17. casum erit yy -x = BD, et 2Xy = AD, hinc per lem. 2.
  18. y3- 3Xx y = b, et per lemm. 3. 3Xyy -X3- a. Si nunc ponal
  19. arcus intermedius Cd aequalis duobus arcubus AC, ila utar
  20. cus AE fiat quadruplus iprurs AC; ergo per secundum
  21. casum erit 53-3∞X Y = BD, et 3X7y - X = AD. hinc
  22. per lem. 2. y Cxxyy + XF = , et let. 3. 4X7 -4Xy
  23. =a. Porro Li arcus intemedins CD aequalis Aaruatur
  24. tuplici arcur AC, ita ut arcus AE evadat quialuslus
  25. ipsius AC; ergo per tertium cassumm erit yt. 6xxyy + xt-
  26. BD, et 4xy -4X Y = AD. hinc lemm. 2. y= 10XXy +5Xty =b
  27. et per lemm. 3. 4Xy -10X37y +XF =a. et ita quontque libetfa

Cite

LBr. 57, 2 · Bernoulli, Joh., fol. 76v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/DE-611-HS-3653099:0152?run=74