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Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 23r

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. 22v); this page is its right half.

The machine reads it as

  1. S. feret ht +5g =0. firret ex aequ. 1 agh = aaV- est = (ex rg. 2) + a W - b5 +, et s+ = aa (W -)): 4 (bc
  2. 1t agh = a) = caa (1o. 7 )(: 4 (b. d). sin agt baa) (=C aast caa )V caa D: 4 (b -c) seu gh = a ()- ci)
  3. Ex nt +5g =0 firret nertih Euu ses h= posio 3) 1g (onc)5--ht: 9 et -het: g- aaso. . 1sb- )
  4. et oV - cld = Falf +br sac. = (a (Yab - sac) + D IbC) (Yab + Vac). ut st = V aaY: A (lab - 1ac)
  5. et oh= af (sab = sac) tas, bE,:, 4(ab Vac) et fiet
  6. =stgh = Bhutt = 5599 = (a - 10) (b) - c1): qu (b.c afr (tab. Yac) +ar ibe j. 1guffaba tuc
  7. ao et Veniamus jam ad explicationem aequationis ulticmae paginae praeceventis, quae satis
  8. aghu ( (- 8) st qu (Bract Z Sab) = a agh tacst, - aa B ( e aorb matcitib. vac) aatile, a act rasa leb talir
  9. Ldagh- astite, taaBEH
  10. et aas t qu (aptiactaz ab) -- aq aer AH,: 4 (sab - 1ac)
  11. Vab lac) +arribe
  12. 2+ hhet=
  13. c qu (tit - 95)
  14. 4qu (tab- Vac
  15. Ergo tandem frV (Tab- sac) + rr Ibc + af, (Jac - sab) = f(Vab - lac) taar sbc
  16. compendii causa sit vab - sac = A et IbC = V, et habibimus aequationes sequentes
  17. qu (Tab+ tac)
  18. St = aar: 4_ gh = ab f + a NVY,: 4B
  19. hhHt = sigg = a adfI, apr: b66
  20. et tandem fr vor + e B vrr + afs abss = aaf t aaqvr
  21. 5= aa invoniamus S et g, siet
  22. 5 = aar: +bt g= abf+ acoY,: 4bh fit =s9 = , a, b5+ aY, : 160Bht = ht
  23. Et = a Hadfr Bar r1): 4D = -59
  24. + = as (ab fr + aN rY): ADM et 5= - aa
  25. adh
  26. EBa CaBEr+avr)
  27. Superest aequatio in qua solae sunt fet Y nempe
  28. = -ahr: Y (adsrtavn)
  29. frDD = r D_ + BD Barr. + adH = aab f + aa VY, seu
  30. y f + a + PBrr- 2aadY =
  31. at +BOrr -2aaBP - 4 a N + qciV: B) r
  32. 4aa
  33. +B- 4a = ab + ac = 2 a sbc - 4 a fbc 2aaD + 4 aV : B = 2aadD + 4
  34. 4
  35. 4aa
  36. -2na B + 42 Raa, ab- ac + 2albc + 4a eoc, sed nulla hinc compendia
  37. fiet f = aa = DY + (a +BBIrY + 4 a(v: b) Y): 2a
  38. =gade
  39. = Z aaor
  40. si si velimus facere f =0 fiet BY = aa seu Y = aa: D et foret g = a V: 4BDh
  41. et F = aavaN: ADb et 5 = - ah: sac et h manet arbitraria
  42. Rspetau Calculies posito f = 0 et ht + 95 =0 EUam firi arVb- aegale (i antaria a ab
  43. a tib Bst
  44. ob B = 7 fit AA = gan seu aerre- Aagut 4, gatu
  45. seusarre = 4(a3), gatr (+ ht vad + StC, ob h= B fit pp = 4aq. seusartb = a gahs it lab Stb
  46. plis aegq. fit Regh= stida = _b, vrat: 4a, ques duos valores aequando sit st = r.
  47. o (P. . Apul P lab e plac)
  48. -ye (aagh+ abst + Cant Fags) iab p. q r abt fa) Btacts saba as t dact
  49. +95 val
  50. E qu af.Y)ab) = 4ab5+
  51. gbYaB
  52. A g5= -ht s = -ht:g = ghrr = ahhlt ,: Ht sit sthH = gghrr + aghat F, et
  53. et fit h= HH- gorr: 4gH et fiet S= fflt + ggrr, : 4g9t
  54. St = - - AH (+ g9rB, = = (a rr (C. b) rasr ( C la b) 9e (u (C. b)
  55. et on - ggnr,: (El = da f(b- CD+ rafo (btac - etab) : (ina Cb. C)
  56. (+:gu = q adss Cb arr b) agr loca tab) trY 2aBr (Lctrab) .4(P- 9)
  57. aq: H = 2 afB (bsac = C Nab): aa (C - b) Y) et tuanescentibus F .E, 9, 5, r, fint
  58. d, = 4 aa YbC (ab ad): a qu Cb - C) et fieret, 1bc =- b +C,
  59. sin fes prasse atrr t ragritaet ast abrr F rasr vab;in qacabs se ele rai cherteord gs e B)
  60. qu Cb-c)
  61. go, part aatislab. tretarobe,- aassatriat
  62. contrahitur ponendo ht+ 95 L0 paagh FabSF a3Fa
  63. qu (Tab + lac)
  64. 4(b-C)
  65. et fit 9 = Ahtt, b - C : aa(V - 10) = a (b) - c1): 4h (b -C). sin IBhhit Ca V1) (. ad
  66. Et explicundo Zet W0 et) fiet X V. W= Y(Sact ab) velb 55gg =
  67. act terrab
  68. Est autem, 3a = r(Nab + 1ac)
  69. Tab- saC)
  70. itaque Et aGh qut B. 15) =- a, afeab - a1) (Nab tac) Ibc (abt actratbi)s: A(tabo tac)
  71. e
  72. et aβ sac + ac s ab = afiac qbe + af ab Baribe = af (Vab q vac) +ur
  73. itaque - aaghqu (a β - a Z) = - aa, ex afrr (ab a sac) + ar bc, : 4 (tab - Vac ))
  74. et itue fieret 4bc = bb + c = 2 bc seu bb. + cC + 2bC
  75. e l) C inttu ali oetitum succede et si catbulus esset bonu
  76. ee= 8bc +9bb = dbb L bb erfit a 3b -C = 2b+2. seu
  77. c _V, 3=212, quod mrirater, si res hvccasspenti sucideret
  78. 1

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2a, fol. 23r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068197:0045?run=74