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Leibniz-Handschriften zur Mathematik LH 35, 11, 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: 0.92.

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The machine reads it as

  1. Mathem
  2. THEOREMA PYTHAGORICUM
  3. Empirice demonstratum
  4. circa rectum
  5. Trianguli rectanguli duorum Laterum quadrata aequantur
  6. Quadrato Hypotenusae
  7. ut horumlatera cd, BG se secent in L
  8. Ecthesis: Esto Triangulum rectangulum ABC, dujus angulus rectus B. dico quadrata
  9. acela lateris AB, et lateris CB simul aequari quad rato hypotenusae AC.
  10. ppapiratio: Super AC erigctur quadratum ACdE, et super CB quadratum BCFGP. Ex E opposito
  11. prua mon-
  12. strata
  13. ipsi C agatur in AB perpendicularis EF. Cum et super ea erigatur quadratum EFCH
  14. Denique ipsiDL sireatur in AL aequalis AM et ex M
  15. ad partes 9 latuseai d geat in ABs agatur porpendicularis MN
  16. Et aequatur ipsi AB. Nam ang. EAF + ang. FAC = rect. et ang. EAF + ang. AEF = rect
  17. ergo ang. FAC = ang. AEF. Ergo triangula EFA et ABC habent eosdem angulos, et agum
  18. loppotenu jam hypotenusas habent aequales AC et AE, ergo triangula sunt congrua inter
  19. sE, seu et EF = ipsi AB. Cemmn etd esi conguua elet ect
  20. itaque ostendendum, quadratum ACDE aequari quadratis BCFG et EFGH simul,
  21. cum quadratum ipsi ab EFGH aequatur quadrato ab AB
  22. sad pri oetendemus sed prius ostendemus HG transire per D. Nam cum angulus DEH sit
  23. aequalis angulo AEF, et DE, EH, ipsic respective) AE, EF, congruent DEH et AEF, ergo HD ipsi FA, et
  24. angulus HFE, angulus ad F ipsi angulo HD ergo et Hic est rectas, ergo, sed angulus DE GHE itidem est rectus ex constructione
  25. Orgo Hd et HG cadunt in directum, cumque D et G sint ad easdem partes et Hd minor quam HG, itaque HG transit
  26. per d.
  27. destali Ceta
  28. Demonstralio onstratio Eminirica
  29. EFGH
  30. catur aqu’aece
  31. DEFL + EHD + DBB
  32. edL t DEFL
  33. aequ
  34. ACDE
  35. aequ
  36. aqu
  37. + EFA + ANM
  38. aqu
  39. edtm
  40. FGL CBL

Cite

Leibniz-Handschriften zur Mathematik LH 35, 11, 15, fol. 1r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068188:0001?run=74