Leibniz Legible

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Ad majorem Dei gloriam. Theorema Arithmeticum, fol. 6

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: 0.91.

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

The machine reads it as

  1. paT. Fsob impar. Fric ergo differentia a-b, impar: e dit-
  2. Ferentia quadracorum a 2 -- - b2, impar: e minoris quadraci
  3. lacus b, par, conera hypochelim. Non ergo a, est par, sed
  4. impar: _ reliqui b, c, LUnE ParCS.
  5. EA ergo a --- b, differentia impar, ex quadeacus: cujus
  6. radix dicatur d: critque d2, ipla differentia a - - - b. Pric etiam
  7. a 2, IImp2T, _b 2, Par: _ differentia quadratorum a 2 - - - b 23
  8. ipar, e ipla quadratus: cujus radix impar, ex mulciplex
  9. 2d d 2: vnde sublato impare d 2, relinquetur par mulciplex
  10. ad d 2: cujus dimidium dicatur e: exirque lacus a, idem ac-
  11. que 2c2 d2 +2ed 2 + d 2: e minus latus b, idem atque 2 c 2 d
  12. 2Y2 ed2, mulciplex ad differentiam d2, Per 2 e2 + 2e, qua
  13. druplum criangulum a latere c.
  14. Acqui b - - - c, est differentia par, e quadratus par: cujus
  15. radix par, de radicis dimidium dicatur f. Prit ergo b - - -c,
  16. idem acque 4f2. Fric quoque radix differentix quadratorum
  17. b2 -- - c2, par, mulciplex ad differentiam 4f2, per numc-
  18. rum, qui dicacur o. Onare 45f2, radix erit disterentix qua-
  19. dratorum: ec eric ipla differentia quadratorum 1682f4: 8
  20. Cumma lacerum 492f2: _ duplum majus latus 48 2f2 F 4f2:
  21. ec majus ipsum lacus b, erir idem atque 28 2 f2 F2 f2: 8t
  22. minuslatus c, idem acque 292f2 ---2f2, mulciplex ad 2f23
  23. per 52--- +, quadracum lateris e, vnicate mulcatum.
  24. Sunt ergo eidem b, cadem, e incer le eadem, 2c2d2 7
  25. 2cd2, _ 292f2 72f2: ex est a, idem acque 2 c2 d2 7 2 c d 2 7
  26. d2: ergo a, est idem acque 252f2 F 2f2 + d2: ec idem ac-
  27. que 282f2-- - 2f2: corumque differentia eA 4f2 7 d 2.
  28. Es ec a 2, idem acque 15 +f4 F882f 4 Y 4f4 F 482f2
  29. d2 F 4f2d2 + d4: e c2, idem atque 45 4f4 = 882f 4 Y
  30. 4f4: e differentia quadratorum a 2 =c2, eadem acque
  31. 1682f47 452f2 d2Y +f2 d2 + d 4: acque ipla est quadratus
  32. 2 radice 4f2 7 d 2.
  33. EK ergo radix difterentix quadratorum a2 = c2, ad dit-
  34. ferenciam lacerum a -c, aequalis, e non mulciplex. Atque
  35. ita differentia quadrarorum a 2 = c2, ad differentiam lace-
  36. Tum a =c, CAVE a = c, ad rnitacem: sed eriam est ve a fc,
  37. ad rnitatem: quare a -c. 8 a tc, Cunc aequales. EF hoc est
  38. abCurdum.

Cite

Ad majorem Dei gloriam. Theorema Arithmeticum, fol. 6. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/827668708:0008?run=74