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Leibniz-Handschriften zur Mathematik LH 35, 11, 18C, fol. 47r

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: 0.84.

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

The machine reads it as

  1. et
  2. et
  3. ul-
  4. u
  5. M
  6. m
  7. dus
  8. ba
  9. es
  10. Sert. 1. Cap. 3. De Ductibus
  11. ses vero sint par tes rectam constituentes, propontionales par-
  12. tibus recipientis.
  13. Nam si (Fig. 9.) gravis AE partes AB, BC, CD, DE, sint
  14. pi
  15. proportionales rectae FM partibus respondentibus FG, GH, HL,
  16. C
  17. Lm, et utraeque partes sint constituentes sui tatius, sintque recte
  18. u
  19. S
  20. FN, GD, HS, Ld proportionales gravitatibus specificis partium
  21. gravis, AB, BC, CD, DE etc. erit (per prop. 4.) rectangulum quodque
  22. Gpropontionale ponderi partis respondentis ut AB.
  23. ut Mo
  24. Ergo et FdCOPRSM figura scalaris ea omnibus rectangulis
  25. composita, ipsi ponderi gravis Ae proportionalis erit.
  26. Porop. 7.
  27. Visdem positis, si nulla sit, pars reupientis, n quam non
  28. varia sint ordinatim ducenda, tunc figum sealaris abit n
  29. sogonium curvilineum duitur, propontionale.
  30. eadem fig. 9.
  31. Ut si quae (in fig. superri) fundo E propiora sunt m gra
  32. n-
  33. vi AE, ponantur etse graviora; utique in quavis sectione ut SV,
  34. diversa erit gravitas, cui inter F N et G0, propontionalis XY re-
  35. spondeat, atque ita smper continuando interpolationem, ut rectan-
  36. gula velut TXG perpetuo fiant minora, donco tandem latitur
  37. do eorum sit connescens, fiyura scalaris desinet m ioyonium
  38. curvilineum NrODAL proportionale ponderr, partis responden-
  39. tis AD.
  40. sogonium curvilineum vocs, quia omnes
  41. rectre ut F.N, G0, seriei ducendorum proportionales (nempe qra-
  42. vitatibus specificis) angulum eundem faciunt ad rectam J. M
  43. magnitudini ippus gravis AE respondentem; si angulus sit re-
  44. etus, vocato Orthogonium curvilincum, figuram scalarem
  45. simpliciter vocabo isogonium rectilincum, et tam scalarem
  46. quam isogoniam carvilineam communi nomme figuram ito-
  47. joncam appellabo, et ipta quae eodem angulo insistunt dicentur
  48. or

Cite

Leibniz-Handschriften zur Mathematik LH 35, 11, 18C, fol. 47r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068193:0095?run=74