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Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 46r

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. 47v); this page is its right half.

The machine reads it as

  1. venit, novum leu tentamentum in nculem pro resolutione
  2. differentialium. Constentus it dus fassiosue
  3. prirui puncti X, coincidere
  4. es
  5. dua Xdr gdq ydx
  6. V. g. si esset proea aaequatio
  7. fieret en casu du dy. + axdx = dyc Axdys posito Ad, X get
  8. Dinter se X et dx.
  9. curvam exprimi, continue variando axest, et cujusque axis initialia tantum
  10. puncta consiterando. sit cuva AB ACQ, sit axis AB Apis AH, et alius FH,
  11. et ex puncto curvae Q duae agantur normales una i Zp in AH
  12. altera Eto in FH. sit AH, a; AP, X; QBy. FId, Z
  13. 7t, v ex jam ex Z ectae HF, L) se secent in G
  14. erit AP: pG: AG = LW: WG: Gq C Ergo Hp: PG= Z_: WG
  15. AP: HH= Z: G et TG: GH = 1oG: GZ sed AG + GWF
  16. =G1o + eo et HG = AP= p GV somitamus aequ. 5
  17. quin sequitur ex etr. _HW + WVF= HF, omittuim
  18. initio HF et HA, sex et AP et FWD
  19. 10
  20. sit Ap: (A P + pG)= ZW:
  21. (GW + 3W) qu= HH -Hp Z GE et eX aequ. 1
  22. Hp. pG GH il in ex ag. 2. per
  23. fint, 1 P: pG qU: H, W0, = SHp + pG2, et ex aeque
  24. 10 fint Hp: (H p2 F pG2) = L2:, HW + HP + p G2 2Morni
  25. restat pG. tolcenda per aequ. (2 et 13.
  26. lemne
  27. ex aequ. 12. Ht = BG (ae: HP) + H1 = VHp + pest. seu
  28. Ap G2. (9W0: Hp) + HW 2HW. pG (ZW: HP) = H p. 7 p G.
  29. 4 + pG: H
  30. Ex aequ. 13 = Hp. eu tep G2 Qqu +HW. Hp + Ap +PG. HP - 2H1 is
  31. seu HI. Zu- PGr. quo AH1S. Hp+ Ap L p G. Ap = 2 HV PG QVO H
  32. + 2HW. ApV jam ope 14 et 15 tollatur PG
  33. ex i est pGt = H p4 - Hp. H + Z H Wo. ZWo. HP. pG.:, elo- HpE
  34. ex i5 est pGr = e p4 + HW. Hp = Hp. qu + 2 HI qW. Hp. PG, :, QW - p
  35. et fet 2Hp. H2 = H p e absurdum est erior in caleu M. Ar
  36. p0 - F9W + HW + HP E PG - ZHW. p + p GrA Ho
  37. il
  38. Ap. HC - pG. Cto :AB. seu H C exp p (Z1G Hp = AP. Hl eS. Q
  39. .tu
  40. pG = VE2. HP P eW HP + H p + HW. Hp 6 3: 2H (B;, P8 - HW. qW. (Ex 3)P i p - H _ : eW - H sol
  41. fi p p E q- 2 p p B. pG. = ZW. HP + HI. M B + A pd ( BG. H Ph (3AW.) Ap, - 2Hlo Zud PG
  42. Ex, fit AP. HUS - HP SHNL pGr = BG. ∞W. sen AP +P4
  43. Eet h
  44. y vel y
  45. Wd F = HF, A = AH- AP CAPG YGZ = )eZ. sene
  46. jam Gq
  47. HP: pG = ZW:, HW - Hp + pGi
  48. (e
  49. 2+ Ap= H HG2. ego ex Y et 8. fit fHW:, F, HP. PQ H1o. 210 - 1, AP. H13: Cd. A
  50. deu A4 sed axissen iL: LA et fiot PE 6 t 9 et 0 l: Y = HW:, Ap. Pg- H1. quo
  51. seu p9 = oW + Hp + H13, :, 3 AP. PQ = H H a
  52. superest
  53. Ex ) et H est Ap. p Q = (Y. I) MO + H S H t:
  54. 1046. l: r = s. Hp - x 1,:, ZW - Hp seu 1H. N = U ZW= H. AP = YrHp- rr HIS. Ergo
  55. seo HP: BG
  56. ut ope 5gg. 8, 9, I1 tollamus HP et PZ,
  57. H p2 ILW= rr HIO,: (l- 1 = (per 8) HW + HS YN
  58. G =(I ZWrrHWD + HWO l HWrD (= 1HI r: U- 1r Cixdevend.
  59. fit (UNo rNIo= HuUNu et si Hol
  60. Wg. v sit Hp: pG = r: l tit X = Z - rV: NFI y - Z+lIV)B. SAM
  61. que est aequ quae aequalio deberet esse identum est erior in calculo
  62. l- 1
  63. in XFIErrLr et = X se y Sitr - b: DV. et fit
  64. Y
  65. YrF) seu v = (y - X) r: Sit rr
  66. H(yrr =Xrr f. Vitrr) seu q = X(F XVD + yir Xrr,: sitrr
  67. seu Pyt = HW = A = qW
  68. paucis res huc redit
  69. H8, Z.
  70. yFitr ((9-X): SIF Er) seu Z = (+ yer y, + X: sit
  71. (y-X)Sitrr
  72. AP X. P2By. B
  73. sitem nyllans vides efficiendi ut res lampatium hac modo redueatur ad
  74. Et Z X +
  75. v = (X y) t
  76. Quadraturqs nam duo raeter duas infinile parvas dus, dx duae
  77. Csidendum
  78. coaneseat.
  79. 1B373 3βaB, elc reddueret ad 1
  80. ubi pro arcum circuli componendo
  81. ippsas
  82. et Z = X SItEr +y
  83. seu
  84. naneu, Ende lerninalee 2
  85. 3 et t
  86. itaque nul juvat, essi velimus
  87. et alla curva obtinea posset, sed tunc opus A pariari, seu A(+) esse focu,
  88. quid sia s , summando componant aliquid
  89. trajectionem, si
  90. scilicet si 11) 2, contipuaretur in 2825 Maut, 2 aequillam et 435 in 39 2A quoritur valo-
  91. 3)4)
  92. 2γ 3
  93. ipsius E
  94. Malim ergo
  95. tentari a Iaquiri: a
  96. copretus
  97. Ae si feculum de ar ingentim
  98. ex
  99. 1. 1

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 46r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0091?run=74