Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 17r

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: 0.79.

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

One image of two folio pages side by side, registered by the library under both labels (also fol. 18v); this page is its right half.

The machine reads it as

  1. cey. 1.
  2. M H aml + 2C + lh. et mt - 1Em lu- 41
  3. Ex priore fiet: m-aml (i at eth. et quadrando m - am,
  4. Fiat expriore m + L M g2 1. C quadrando M gl M + is t m , 41+
  5. -25 1. + dlo.
  6. + 52.
  7. Ex aequatione posteriore fiat: M- 1tM L at 1
  8. Expriorefiet m - aml 2l + lh. et quadrando: m - 8b m3 + 161 M pi 4l + 4lh+ lL V
  9. = X collatisque duobus ippus mt valoribus, fiet: Dn + 151C ( + 4 17, , (2+ ah + BK + 8l m - 16Cm
  10. C - amt + 4 pbl + th. Ergo f m F 2l B X modo qua dratum ab X, sit
  11. majus quam 6.
  12. jm
  13. m + r m+ 5, + m + +, m + co, dant
  14. m+ + rm + rs m + rst m + rstco pa
  15. + rt
  16. + Yc0
  17. + s +
  18. r0
  19. Ponatur et ++sAco
  20. item rsterscortcot sta po.
  21. Ergor =s - + - c, quo valore in posteriore inserto,
  22. fiet: - 5+ - 5d +sco - 5 0 - stco - 5C0
  23. (- S+c0) - tc - +c0 (+ stco)
  24. Et fiet ponendo rursus: 452 t + st + s + 5 +c0 + 5cd + trco + +co
  25. Hoc duobus effici modis potest, tum ponendo duas radices simul, nihilo aequales tum
  26. Quod malim ponendo ex ordinata aequatione inde extrahi posse radicem, vel
  27. sallem affectam, id est conferende ipsam cum alia
  28. nempe s
  29. +co + +c0 H
  30. + e+ +S A 1c0 +a 0.
  31. p. 3+ +e..
  32. conferatuo cum 5 + b + Bs
  33. et tc + V
  34. et ordinando
  35. + + co
  36. + + C + cor sive F c0 + +c , yt + Va VF+ tors
  37. 2+ teo + co 7
  38. (+YFO (+Ct)
  39. + + tco+ y +c 0. Jam faciamus:
  40. +4+ 2t c + 2t a +co + cot +4 ho +32S to cC)
  41. 4t + 8 teo + 4co
  42. 4 +7 + 8 tCo + 4co
  43. debet ergo ex 14 + 6+ co +1IF co + 3t Cd + co + extrahi posse radix.
  44. sed haec prolipiora, et satius puto duas sumere radices aequales nihilo sive
  45. tunc ex aequatione D (et (4 t a) (tCo+ 1 +(FC 0
  46. 0r. (43 - 13) (+ t c- 2t c) (= +c0) + t2 a (+ + cod
  47. P 5- t.
  48. +2a
  49. Ergo in aequatio proposita fiet. Tantum
  50. Quod ideo veri commodissimum, quia
  51. pro Y substituatur co et pro S substituatur
  52. videtur ob exempli raritatem
  53. Edus et quartus, fier:
  54. jam ex aequatione proposita faliumus:
  55. mt - 15 V m - ++ 0
  56. Pit p 7 L3P- B i p - pB OP. 1BI. Ergo psu D (2 P. 512 . faciamus alidm. m B
  57. 25.
  58. Unde m pi 4 X + 2l.
  59. + c..
  60. licer aquationem pragositem epatarie in masi ctamus aliam. m -C 1
  61. X 2 613
  62. + d
  63. 0.
  64. m+. (+ cot m (+ cot +fco
  65. + cot
  66. =12n, mundo (, l9m - tet - 40
  67. = cot)
  68. = 41 go. Quam cumfacitia proposita posumus conferre siet Enebitur
  69. + +co)
  70. valor tum ipsius h tum ipsius 9. Unde unam ex Tadicibus
  71. possamus eligere, nempe sed non sufficit, quaeritur valor
  72. is ex tadiabus, rensui ut lel c

Cite

Leibniz-Handschriften zur Mathematik LH 35, 3 A 16, fol. 17r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068229:0033?run=74