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Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 2v

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.

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. 1r); this page is its left half.

The machine reads it as

  1. Restat ut videam pro plena poblenatis propositis solutione possitne effici pot
  2. tam quadrato. quadratus, quam quadratus simul sint dati, quod tiea, si
  3. aequationem hanc V- itq qu +e v 1+ 2l9 - 292 - l
  4. rendemus tatem, ut V pro artituo simita, 4 inveniti.
  5. 1+ . l + 1ol + 49.
  6. queat: Fiet + f 2 lV + 1ol v + 4qV p + + 2lq - 25 - 1. poue
  7. V
  8. et restabet
  9. 7 219 - 29. Pone Z5 47.
  10. poterunt omnia dividi per g. et fiet aequatio:
  11. dato
  12. 1
  13. 1 2l - 29. Esto jam
  14. + 210
  15. ex ilem ) ex +) e Namcrg datus, Ent es exempl causa d.
  16. fiet v Xl. per priorem positionem, eoque valore in posteriore substituto, fiet:
  17. (4) X (+) C B d. fier e p X (4) d. et v
  18. jam vBZ - β., et seu Z H 2 10 Erit 2
  19. hac methado.
  20. Sed hinc jam video rem absolute efficimon
  21. XC
  22. X XI
  23. XC+)d
  24. X()d + 2010I
  25. datus, nisis quia V jam datur Ergo in aequatione initio reperta pen seram
  26. valorem ipsius B. fiet: + F 2xB + 10l X + 4qXl + + 219 X +
  27. s
  28. sive + f2Xt rol x F aqXlp, + F atq L +X ()d
  29. 290
  30. -29.. (4V. 2
  31. f sie. 2qX (+) .9d + + 2lgX (F) +f 21q 5 L+ 2XV + 10V a + CXH)
  32. sive 4 s- 1F . IX q. + O p Ext r 10lX + l X (4) P
  33. 5) tra.
  34. 1.
  35. (F)4 d
  36. - 2X (+ ) ad
  37. - 2x (4) 2d a erit g+8H S+ DI+ 8.
  38. sunt autem X et d; et l. ac per consequens etiam D et C. numeri
  39. dati, quare si 4Dl +. O evenit esse num erum quadratum, tunc effici
  40. potest ut utam quadratus quam quadrato quadratus sunt dati Illud
  41. vero manifestum est, quia in aequatione 8. neque X. neque d. ad quadratum
  42. ascendunt, dinc semper effici posse, ut alterutra earum sit data, item ut datam
  43. ita ut summa eorum sit potestas quaelibet, et summa quadratorum ab
  44. tam summa quadratorum quam summa quadab, udom sit potestas gradu
  45. Videndum tamen superest
  46. habeant rationem inter se. Hinc ettiae posse mani ex hoc uno problemate (16) si ponatur
  47. aTies numeros invenire
  48. ipsis quadrato quadratus. Illud tantum videndum ex an effici queat ut
  49. dati.
  50. tonatur v H Z. (3 fier: + + 21Z + f 2l ( + 10l X - 1ol. ( + 497 + 4487 4 l9 39. (a) summ hameroni X. Quadratus, primam conditinem.
  51. Pone ++ 2l - 10lB p 17 fiet (1
  52. + +. 1Z + 101Z + 19Z + 491
  53. 10
  54. 1+ 2V + 10) + 4 47 + 41
  55. )
  56. 4... .
  57. sit
  58. O

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 4, fol. 2v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068001:0004?run=73