Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 87

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.

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

The machine reads it as

  1. nire
  2. rei
  3. UI
  4. ex
  5. al
  6. ino.
  7. 12
  8. B in
  9. ma
  10. 1X.
  11. UIM
  12. UM.
  13. nuC
  14. 23
  15. B0r
  16. et
  17. eun
  18. in
  19. 10c
  20. ECHII
  21. E1
  22. AE OV A F +O N V Mt.
  23. EtsFC. == 729 N. aequatur 18954. Phma major incer extremas est V 729, id est 27. aggregaruIt
  24. Fundae quaria i est 26. 8 fit 2 N. secunda ex eadem serie.
  25. H E O R E M A II
  26. AAO_ ATTKII S.
  27. F A cubus =B quadr. in R, aquetur B quad. in D: LuI Gat COn-
  28. tinue proportionales geatum prima minor inter extremas est B, disteren-
  29. Dala prima minore inter extremas, ex differentia secundae ex quartae in se-
  30. rie quaruor continue proportionalium; invenire secundam.
  31. Sic dara B prima minor inter extremas, differentia vero secunda eC GuarEX D. OpOr-
  32. cerinvenire concinue proportionales. Sir le cunda A quarra iDIEUE CrIF A + D, (0ldo 2y-
  33. cem sub guadraco primae de quarta, aequatur cubus e lecunda; quare A cubus aequabicuFB
  34. quad. in A, + B quad. in D, e per ancichetim, A cubus- B quad. In A, xquabitHEB
  35. quad. in D, uc est ordinacum.
  36. Si 1 C. = 64 N aequetur 960. sune quatuor continue proportionales, quarum prima est 64.
  37. id est 3. disserent vero fahia quarca 3C C id est 15. e fit 1 N. secunda ex serie proporcionalium
  38. T H F O R E M A III.
  39. A N ∞ YB O A O Y.
  40. TB quad. in A = A CubO, EGUCTE B quac. in D: SUINE QLATIOF CONEMUC
  41. proportionales, quarum prima major incer extremas est B. ditterentia
  42. vero secundx _ quartx D, e Ac A lccunda.
  43. Ex LCcCTICO:
  44. Data prima majore inter extremas, es differentia secunda ex quartae in serie
  45. quatuor continue proportionalium in venire secundam.
  46. Sic data B prima maior inter exrremas, differentia vero se cundae _ GuarFa D. O pOrECE
  47. invemre lecundam Sic secunda A, quarca ixicur erir A - D, Colido aurem sub quadeato
  48. DEIIX _E qUArEA, EquaTUT CUbUS C Secunda: quare A cubus aequabieur B quad. in A, -
  49. B quad. in D de per ancirhetin, B quad. in d - A cubo, aequabicur B quad. IN D.
  50. St729N. = 1 C aquentur 7 296. fan qualuor concinue proportionales quarum prima est a 729.
  51. differentia vero secundae e quareae S id est 10. e fic L N. secunda ex serre proporrionalium 27. 18 12. 8.
  52. Pocest antem ea febaum esse, ut in duplici quaruor commue proportionalium serie quae se-
  53. Guitur.
  54. 1
  55. ITT. IV.
  56. N 59319, 195. V 24375 125.
  57. 59319. 36. N 624. 8.
  58. Stante eadem prima majore inter extremas V 59319. e eade asperentia secundae ex quarta 30.
  59. secunda hic fic 78. illIc 195. Sic stance eadem prima 36. eademque differentia secundae ex tertia 5. pro-
  60. 36. 6. +
  61. 36. 30. 25.
  62. F V
  63. tia secundae d Guaca D, X HE A secunda.
  64. Ex ZCreHICO:
  65. Penitur duplen ser tes tr proporcionalium.
  66. Consticuriva aequationum cubicarum in quibus affectiones sunt
  67. sub quaarato.
  68. Lnes, iildem Fercretmus constane, quibus in affectionibus siblatere,
  69. x aurem cubica aFFectiOHDUS IHD GuACTAL BOVOILIHEIE EGuatO-
  70. elt

Cite

[Francisci Vietae Opera Mathematica] Francisci Vietæ Opera Mathematica, fol. 87. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/845634801:0103?run=74