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Machine transcription of the Leibniz Nachlass

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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 134

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. F. L ML E N D A F FO A
  2. In quadratis affectis, homogeneum comparationis invariatum conssti-
  3. to: in cubis ducitor quadratice: in quadrato-quadratis, cubice: in quadx2-
  4. to. cubis, quadrato. Quadratice: in cubo. cubis, quadrato cubice: & icadc-
  5. inceps.
  6. 1t
  7. Fromogenea sub gradibus adfcientia negate, in homogenea sub oradi-
  8. bus reciprocis adficientia aftrmate eranscunto: c contra, adficienria 2d.
  9. Trmate in aFhicientianCgaTC.
  10. TTI.
  11. Coethciens adfectionis lub lacere, invariata contistat.
  12. Coethciens adfectionis sub quadrato, ducicor inhomogeneum compa-
  13. rationis.
  14. Coethciens adfectionis sub cubo, in homorenei comparationis qua-
  15. dratum.
  16. Coefficiens adfectionis sub quadrato. quadrato, in homogenei compa-
  17. rationis cubum.
  18. Coëtsiciens adfectionis sub quadrato. cubo, in homoseniei comparatio.
  19. nis quadrato- quadratum. e ita deinceps.
  20. Acque ad cognicam radicem porestatis ita noviter ade quata, dum appli-
  21. CABIEUIE HOIOSCNCUI COIPATALIONIS PCTEIMENS ad XGULALIOHCM QUX PFO-
  22. Ponebatur, resticuere lacus de quo primum querebatur pronunciato.
  23. Plane quecunque magnitudo ad novam quarendam radicem applice-
  24. tur, ita uc ex ea applicatione oriatur radix de qua primum queritur, li lub ca
  25. specie dirigatur propolita aequatio, ee le cundum artem eransmutetur, sem-
  26. per adtectiones que crantnegate, transibune in adtirmatas lalra numero-
  27. rum Cymmetria: le dideo conrenientios est applicatio homogenei compara-
  28. tionis, ne forte accidens tractionisnovam rurlus exigat reductionem in A.
  29. richmeticis, at in Gcometricis, talicius applicatur magnitudo homogenca
  30. Quadrato radicis de qua quarirur.
  31. PEOxOnAuE A cubus = Bin A quad, aequari B in Z quad. n 2Z estO A. E cubus F B
  32. quad. in E, aequabirur B quad. in Z..
  33. C A P V F Ht
  34. Dc Analtrophc.
  35. Aut quemadmodum ad versus vocum Aupiboxias in aequationibus cor-
  36. rclucis, la aata racice unius habetur alierius nocitia.
  37. Lmutatio, itainctituta, ut gux prima proponitur requatio, ca ope lix
  38. Correlatx per irregularem climacticum descensum, re ducatur ad depressio-
  39. rem, ideoque magis explicabilem. percinet ad vicandum tanquam in xe qua-
  40. licaribus inverse nesatis accidere diximus, amphiboliam, e dysinechanian,
  41. in cubicis, quad. cubicis e exinde per binos alternos gradus climacticis.
  42. Ouodenim ad quadraticas, quadrato quadraticas, ec exinde perbinos al-
  43. ternos gradus climacticos attinet, carum re ductioninon protcicanastro
  44. phe, verum recurrendum est ad C limacticam Paraplerolin, de qua dicctur
  45. luo 10c0.
  46. AN2
  47. A. Lauropheeltaequationummreeala Ilas Correlatas erant

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 134. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0140?run=74