Leibniz Legible

Machine transcription of the Leibniz Nachlass

Search the Nachlass

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 165r

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: 0.78.

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. 164v); this page is its right half.

The machine reads it as

  1. Assumo y: a = loXX + 12Aa, 1, 20X + 22 aa
  2. axa 12
  3. Ita per 1 et 3fiet
  4. Explicentur y et X per a
  5. 330rV + 31RZ + 310 av f300aa
  6. 420 vv + 4uBZ qu ap + quoa a Et sit
  7. (4) 10. 510. 510BV + 12, 6016012Z
  8. 20.510.510 bP + 22801. 6012
  9. quos duos valore) ipsius 3. aequando fiet
  10. aequatio nova (5) In qua possunt, occuriere 4 13Z 17. VBZ
  11. Tollamus v, VZ, V, ita ut V non assurgat altra secundum gradum
  12. NrZ, VZZ, BV, ZZ
  13. ob V fiet 1G2d. siosto = 10 ga = 10. 420 - 29 320=0
  14. ob V fiet
  15. +0 (1. 510. H - 255103,0 31 of . 10. 410 - p0. 310=0
  16. persicusto. TH. 20r 5id h0. 3H aoseu 10.4IL- 20. ao
  17. Ponro comend Cssa ((.1100 Porro compendii caussae
  18. Ob VZ fiet
  19. pro +1. 400 H12. 400 +10. 410 +k. 4
  20. -20. 310 = 2. 40
  21. 20. 300 -12, 300
  22. ponatus occ. 400 200 700 090. 410 (210. 410
  23. uibi tamen ob bes aegu. quibus
  24. Si +11. 400 -000100
  25. +10. 401 +L. 401 +1∞. HI +12. H1 410. 20
  26. 220. 301 32. 301 f2o. B11 ∞2, 311 = 20, 320
  27. 001401 troj 40 oll. 4i1, 2I1. 411 020. 4
  28. infra certocasu ey orp
  29. v, v Z destruximus fit so20 = 0 et 010 = 0 et o11 =0 (∞) m atabeb
  30. Aequatio ergo exvaloribu, aqaionum 2 et 4 aequatis habebut hanc fornam C DV + D aV + 8 a = 0
  31. ve
  32. ut sit coefficiens lpstus 2
  33. et erit O = 6(. 2. 400 Z Y S10. 0B1 ABI a 2 tactoga L
  34. 512602.402.
  35. D = Sci. 211. 4117 + 5o. 218410aZ
  36. uit comprndio C- br t2oZ Z + o,. qolazu. +. sro. quoaa D. aui +. B0 404Z Z G = Bor. quqe 0+ 101 Z +Be quodni H
  37. Ex aequ. 8. fiet V
  38. +1Cg-40E
  40. quaeramus valorem ejus quod vis
  41. continetur, ex plcande O, D1Z
  42. eritque ((DD - 404)7 ((ed1B1. 4 1 Z , 2. B,B BH. o ma a aBa neE
  43. Lagbo. Be. 402. gd .d a J. 701. Bor. 401.902.. orB tor 162...
  44. sit datu fermula generalis sundata:
  45. v qoyt. qu oe a tt ato in. 4p 1 0080 horria
  46. 4. 702:B q.
  47. xmazanaaZpaZ q coincident termini ultini seu absoluti. o Z fit 500. B0o t 100. do. Li S0. B0v. 401 a
  48. identificetur Formulaesvinculo inclusa. ex ob ZZ et 3B, seu per Requationem inter duos cbefficientes ipsius ZZ, et aliam
  49. haec multiplicata per 4. 60. e. 40 o Ha tar intu et en elidisuts I Acpliar coifficientium issuus ZZ
  50. multiplicata per a). Ites positis
  51. inter duo) cdesicentes ipsius Z, habebamtur valores simplices ipserum 420, et 402
  52. pps qui in pice duabus aequationibus nec in se atte invicem dicuntur. Superest
  53. unea aequatio snter solfficientes insios Z+, in qua substituende valores repertos ipsorum 400, 420 402
  54. restabit aequatio un solvenda, quam segredientur 401, 410, AC, inqua bae incognitae ascendent ad seuodim
  55. tradum. QGortasse ob abundantam arbitrariarum seu in Quate incertarum romui p, nova hypothesin com
  56. modam assumtam ad unam vel binas sempliles reduci potast.
  57. Et plarimum contrahetur calculus,
  58. si in desa formala abesset qt seu esset l =0, ita enim possemus facere Si1 = 0 et 802 =0 vel
  59. et 202=0. ita tribus tantum indigebimus aequationibus
  60. comparatilii formularum, eaeque etunt omnes simplices. Hunc orgo casum, ubi abest ut
  61. quo quod eodem redit, 21 =0
  62. nam quia jam posuimu aturae sentrarum absolvere suffecerit. Et pervrode est ac si intio sentim praeter Temino
  63. V, V3Z, V, destruxissemus 7t, et 7 3 et _ manente C= I: 220. 43 Z +510: 001. 1ga Z + 510. 000 70 a
  64. cot. 002. 402
  65. Et ex ag. 10 fiet
  66. S(DDr 4O8) = Z(4. 6018,0. 401, 120423 + 6∞6,0. H0. H0. act Z - 4. 700. 6d. 100. 431a - 4. 100. 606. 400 400a
  67. fieret 3. 601. 210. 410, 22 et = 601. 201. 401 73 + 601: 200. 400aZ2
  68. 4. 102.801. 48. 402. 1. +)1.601 401. 401
  69. sisdata tomula gererdli ana spaus as a nultilicetur per (. quo doo. 4o oo, podibi poriori identisicanda
  70. L (- 4. D V00- 400. Vuom7 - 4 Jo0. 800. 40o Jas na ZZ- 4. Hu Bov. 4. 400 parz 4. 100. 600. 400. 1x at )
  71. Ex aequatis cz, fiet 801. A0r a500. 409p. et t Ex aequatis Z3 fiet (pro So1 401 a spostituto prius vatore invento
  72. fiet 820 420 + 702. 4= 500. 400 m Et ex aequatis dZ Z (pro 601. 40ia substituto mis valore invento aequ. 1. Hiet
  73. 810. 810. 40. 410a (4 trop. 701. P00p 500. 400. 400 p - 4. 508. 820. 400. 429a f 4. 702800. 400. 402 a -- 4 7u0do, 1o 3uo n
  74. in qua equ. pro pror 420 substitu chod ex aegu. 12+ Vulorem 500, 400m - 502 AP, ip, fiet
  75. 6102610. Aiv. qa 4 501 (Pp. n) 600 ita
  76. 100 4oep 4600 100 5 40ot p: A a f 4. 6go. 100. 5od tora - b
  77. G HIS agp beS SoI. AB dip. 1 4. gdo so01do (Ga
  78. et eadem ratione in aesp. 13 pro 502. 402 ponende ex aequa se vatorem qu
  79. p
  80. Eb fiet 403
  81. Et ex aeg. 13. erit 826. 420+ f02. 462=
  82. 13: e 609. 40d. 601 aa p (502 - 500)
  83. nm seotdum en per stad, fia tuiau 8B a1B. 2 q0 =
  84. 4, L. sp. 400aC
  85. 700Bo anp + folBop
  86. =0, et habeatur aeqa si SH = Si sit 80, =0 et 700 =
  87. quos duos valores aegnanoo tur bBio. Ba 10 aap = 4. 800. 405 (700 Saa
  88. uae
  89. hadou y
  90. inii indeo non licere
  91. factit 2140 seu
  92. 12. 41- 22. 31120
  93. senlo. 4u - 20. 31 =0
  94. firet 10. 20r v2. 17)
  95. quod fingere licet, quaecum
  96. st ratio 400. xd 3diter
  97. +id 4uD rattor +. 102
  98. 22. g1B 202 7 30
  99. 278. 20 802. 182 . 102
  100. fiet 610 614. H0. a
  101. W. 4i0. i 900av Bo1a X.
  102. ustiit dilus
  103. ponamus 0 quud in data fotmula facia effici potest

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 165r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0329?run=74