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[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 107

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: 0.81.

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The machine reads it as

  1. arlus
  2. Con
  3. EP
  4. est
  5. 3Pd
  6. ead
  7. b0
  8. 1813
  9. ied
  10. 12ti0
  11. F1112
  12. lateti
  13. e1
  14. va
  15. 14
  16. Caciet
  17. mino
  18. ot
  19. pel
  20. 1aCe
  21. A OV A Y LO N VM
  22. Placeat extibere Formulam aequarionis cubinegari de homogeneo adfectionis subla
  23. cere, ue sic radix de Pvel C explicabilis. dixero rquad. -L. C quad. - + F in C in A = A c1b0, C
  24. quari F in C quad. F C in P quad. de Heri A, F vel C.
  25. Sit F 2O. G 2. AL N. formula aequacionis erit Y24 N - LC, aequabitur 240. explicabilis de
  26. 10, vel 3
  27. In concradicencibus, coefsicientes sub graduales proficiscunur ex applicarione ditte-
  28. cencie poreltarum, ad aexcegatum corum quos sustinen coetticientes gractuum.
  29. Hlomogeneavero dae menture, ex applicatione asgregaifactorum reciproce, dpo
  30. duum aggregarum: id aurem quoque obicer est demonstrandum.
  31. L O B L E M a TI.
  32. Vacum Conradicentium equationum consticutionem ex Cyncrili 18.
  33. HOlCCTC.
  34. PEOPONAEUEA pOtestaS L B coëtticienre in A gradum, equari Z homogeneo. EcrursuS
  35. E porestas = eadem B coëtticienre in E oradum, eguari eidem Z homodeneo.
  36. Vnde par existic gradus et par porectas. Oporret ex synerili carum equationum con-
  37. cicurionem agnolcere.
  38. Ouoniamisieur que uni equantur equalia suntinter se, manifestum eR. A porestarem
  39. L B coësticience in A gradum, equari L porestari = B coetsicience in P gradum. de per
  40. ancirhelin E porectarem =A porestare, equari B coetlcienei in F gradum = B coetE.
  41. cience in A gcadum. leaque omnibus per L gradum + A gradu divi(Is. = poccM.. - A B
  42. aquabicur B coëthciedci.
  43. Eractus F a Bradtu
  44. Mu eso Dedehicets suboradualis, ex applicarione difterencia porestarum, ad
  45. SBregarum eorum quos sustiner coetlciens graduum: uc est contticurum.
  46. Porroquum A porestAS L B coetfciente in R Gradum, XGuCTE Z homosenco.
  47. In locum B coëtsciemis, Subrogecurjam agnicus ejus raloc, videlicer ro
  48. adus + a Er actu
  49. _ CA (UBEOBALIONE RGUATIOLCFOTMETUIT. CrBOA POrCstAS L E vocnn a poreaue in ABcadtum,
  50. aequ. Z. homogeneo, hoc est omnibusrire ordinacis avocelur in e ea e soeluie in a eradi X qu. L
  51. homogeneo.
  52. N Scadus t a Pracu
  53. Oricur ergo Z homogenea, ex applicatione aspresari factorum reciproce d porectate
  54. radicis unius, in gradum alcerius, ad pradictum cui alcera applicario facta eAt graduum 20.
  55. Fregacum: ur es secundo loco enunciatum.
  56. In inversis plane negatis, coethciences suberaduales prosicilcuntur ex applicarione ae-
  57. sresati poceltarum, ad agcresacum eorum in quos coëfticiens est oraduum.
  58. Hlomocenea vero datx mensurae, ex applicarione differencix Factorum reciproce a
  59. poreltare radicis unius, in gradum alcerius, ad praedictum cui alcera applicario facta est
  60. Seaduum in quos coetliciens luberadualis eAt, agBregRTUM.
  61. Idem quoque obirer est demonstrandum.
  62. R O B L E M A TTI.
  63. Varum inverlarum aequationum consticutionem, ex syncrili agno-
  64. PropONAIuE A pOrectaS =B coetscience in A gradum, aquari Z HOMOGCNCO. LFTUI
  65. lus eadem B coitticiensin E. gradum = P poreltare, aequari eidem Z homogeneo.
  66. Vnde incellIBAnEUE A eC F pares gradus, acque adeO parES POTCNATES, OpOTLCAEAEeM
  67. equalicarum harum consticrionem agnolcere. Duoniam iBitIEGUX UnI LGUAnEEX qua
  68. la sune incer se, manitestum HICCx IIS QUA PTOPONNEUIT. A porestarem =B coelticien
  69. in Agradtum, aequari B coetlcieni in gradum = P. porestare, de per anrichelin A pOrC
  70. atem + E poreltare, equari B coetlicienri in Apcadum Bcoelsicienre in L gc2.
  71. dum.
  72. ciene.
  73. equabitur B coithi.

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 107. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0123?run=74