Leibniz Legible

Machine transcription of the Leibniz Nachlass

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[Ps. 1], fol. 159

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: 0.85.

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

The machine reads it as

  1. Equa
  2. nodo
  3. ajore
  4. reume
  5. Toblem
  6. nC, d0
  7. m Aqua
  8. Can
  9. D
  10. ee dittet
  11. 1
  12. octerie
  13. at
  14. COMMEN TARLL TN LEBRAM I.
  15. 259
  16. In qua si uerinque extrahatur radix quadrata, habebitur 2y ∞ 3
  17. _ EC y ∞ 1.
  18. Cxterum inrento utroque numero incognitox e y, quonian
  19. promajori qualitorum polueramus x- L y d pro minorix - y:
  20. exit major v 7, et minor ∞ 4. EcColucum eric Problema.
  21. Aique ita reducendo illas, efficere oporiet, ut rantum una re- I
  22. maneat, aequalis alteri cognitae, aut cujus quadratum, si ve cu-
  23. bus, sive quadrato. quadrarum; sive surdesolidum. sive qua
  24. drato-cubus exc. aqualis sit ei, quod provenit ex additione vel
  25. subtractione duarum plurium ve aliarum quantitatum, quarum
  26. una quidem cognita sit, reliquae autem composita ex quibusdar
  27. mediis proportionalibus inter unitatem es dictum quadratum,
  28. sive cubum, sive quadrato quadratum, esc. multiplicatis per
  29. alias cognitas. Quod hoc pacto desieno
  30. Z ∞ b, aut
  31. e
  32. Z∞- aZ.+ bb, aut
  33. 3∞ F a Z
  34. F bbZ =c3, aut
  35. (+∞ a Z3 +- bb ZZ63Z. + a+, gc.
  36. Hoc est, Z quam pro quancirare incoonitasumo, est aequalis
  37. quancitari cognitx b. Auc quadratum linex Z clt xquale ci, quod
  38. prorenit suberahendo a Z ex bb: quarum quidem bb coenita est;
  39. sed a Z compolita ex Z media proporcionali incer unitatem et
  40. quadratum ZZ, ut supra explicarimus, et ex quantitate cognita a..
  41. Aur cubuslinea Z xequalis est ei, quod provenit ex additione de
  42. Subtractione erium quancicatum a ZZ, bbZ, ec c3; quarum qui-
  43. dem s3 cognita est; at b bZ compolita ex Z, prima duarum me-
  44. diarum proporcionalium inter unitatemm ex cubum Z3, ec Cx quan-
  45. citate cognica bb; ac denique a ZZ compolita ex 2Z, sccunda
  46. dictarum mediarum, _ ex quantitate cognita a. AEque (iC de
  47. CXtErIS.
  48. Eibi notandum est, per quantitares cognicas, intellisendas esse
  49. Cas, quae in qualtione rel datae lune, vel per certas operationes
  50. dacarum quanciratum, jam traditas _ notas, Sic Praeparatxe lunc;
  51. uc pro cognitis sire datis sine habenda, acque guxlitis sire inco-
  52. nicis aequiparandie.
  53. Sic cum ponitur Z ∞ b, indicatur lineam incognitam, gux
  54. Der

Cite

[Ps. 1], fol. 159. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/175905688X:0181?run=74