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Leibniz-Handschriften zur Mathematik LH 35, 4, 15, fol. 1r

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. 5v); this page is its right half.

The machine reads it as

  1. 29X6. 167.
  2. Invenire Triangulum Rectangulum
  3. in numeris cums area sit quaoratus
  4. Aio id problema esse imporsibile.
  5. inter varias demonstrandi rationes hanc reperi
  6. rucherrimam, quiatmultas alias praeclaras proplositiones
  7. aptissimam ducit
  8. Prop. I. Si sint duo triangula similia, et latus
  9. A’unius fit multiplicatione lateris homologi alterus
  10. per aliquem numerum, (qui dictu a Mono
  11. etiam arca illius fiet ex area hujus per ejusdem
  12. rngu quadratum multiplicata.
  13. Nam areae triangulorum similium
  14. sunt inter se ut quadrata homolo
  15. ctorum laterum, adeoque si latus sit
  16. multiplicatione lateris homologi
  17. per aliquem numprum; fiet quadra
  18. tum lateris multiplicatione quadraet
  19. lateris homologi per quadratum ejus.
  20. dem numeri. Ac proinde, idem
  21. est in areis Triangulorum ipsorum
  22. Prop. TI. Si area trianguli trectanguli primitiv
  23. in numeris integris, quadratus esse non potest; etiam
  24. derivativi in integris, imo et trianguli rectanguli
  25. Cujuscunqu in numeris fractis area non potest
  26. esse quadratus.
  27. primo Nam d Triangulum primo
  28. tivum et derivatinum sunt similia,
  29. ergo per prop. 1. area primitivi fit
  30. ex dinisa areadernitivi per quadratum
  31. numeri derivativum metientis. Ergo
  32. si area deliitivi est quadratus, etiam quod
  33. ea per quadratum divisa fit, nempet
  34. area primitivi erit quadratus. quod
  35. si impossibile ostendatur etiam arsam
  36. dervativi quadratum non esse posse
  37. palet
  38. Trianguli rectanguli in
  39. numeris rractis latera reducan
  40. tur ad communem denominatorem
  41. umat
  42. decundo

Cite

Leibniz-Handschriften zur Mathematik LH 35, 4, 15, fol. 1r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068319:0001?run=74