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Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 95v

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: 0.83.

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One image of two folio pages side by side, registered by the library under both labels (also fol. 96r); this page is its left half.

The machine reads it as

  1. Superesset investigandum, cum habetur fr9thayt ky elius tedydu = 0
  2. ut si fiat E m + ny =0 unde X am +duy r atus -0 ducatur in ps pary+t dy
  3. fit pdm + pan +pndy
  4. +amrus
  5. fgr gqy Fhgtus + tequus telgydus Aequydus.
  6. nb =eq eu g- nt: e = pam: f = rdn: H sit dn = fut: L r - edm . nk
  7. umatuur solubilis jam inventa: m +ny +pdus, quae multiplicetur per r+ ty+ ndus
  8. fiet mr+ arus +prdus
  9. +mtus v
  10. Antgus L ptlsdus
  11. ~ syt gqy +hqdys tRquus Alquydys teg aydus
  12. + nydus + Wp dydu fiet mr- 59 nt = kg W0p = eq
  13. seu im = fg: Y n = kq. t p EG: W. Ex yfil r:t + Lff.r = Dg habetur t:r aequature quadhalica
  14. Ex
  15. + mvodus
  16. Ex du fit (eq.W +10 59. Y = hq datur r.1 per aequationem quadraticam
  17. Tandem
  18. ob ydu fit t ef: W + WKq. t = lq. Et datur t. u aequatione quadratica sed ducendo arvicem
  19. Cns XB Y B KB+ aaf: β ~ 9 seu KB(B agB + aas
  20. seu ββ = aq B + aat seu B - aqe D = 1aagque = aat) de β = a9 + a Y (9g - 4H), : 2k = r. t
  21. t: r et r: W0 habemus +: W adhuc semel
  22. t: r = ag + a . (99 - 4 4FK), : 2f
  23. AKK
  24. W: r = a h + a (sh - 4ef), : 2f
  25. t: W = al + a YU - 4 eK), : 2C et multiplicando + : 1o per W : r fit
  26. at + a t: r. = a aa , l + s(u - 4K), h + tChh - 4 es) = AG a, 9 + Hgg - 4 fX)
  27. su (a, lA + t...; h + f. ) - 9 = L(gg - 4 fK) et fit
  28. aa V (iL + s.. ., h + f.. . .) - g a (L+ S. . ., h + t: : .) = - 4 fK et habetur 9 per reliqua
  29. namfit g = aa qu (L + ((H- 4 eK), h + (hl - 4e5) + a f K, :, 2, L + ((- 4 ex), h + (hih - 4 es)
  30. aeet
  31. Aliter L dita est f + gy + hdy + kyy + lydys + e dydus = 0 et m + ny + plus =o seu dus = n +ng, ip
  32. tt sp + ge - hm ns fPp + goppy + hpp dy + K ppgy + lpp ydy + epp dydus pdus = -m - ny
  33. et ppaydu = um - amny. +gy fit Spp +grpus Ee -hpm- hpnys + Kpp lpym-lxyny temm-remny + nngu
  34. fit +spP + oppu _- lxngu = 0 quod differentiandum, et hinc tentanda solutio,
  35. hum
  36. TK PP
  37. +enim
  38. =hon
  39. remn
  40. nngy
  41. sed quia id prolixius, resumamus mtnytptus multi
  42. plicatum per r+ty+ Wy, et in quodam loco aequa
  43. tionis datae, nempe in hdy substituamus valores ipstus dy
  44. et rursus alio loco ut in lydu, ita plures habebimus
  45. ce quationes compinandas inter se
  46. quaptum ed agendum, ut sint su
  47. quicutum id agendum, ut sint sufficiente
  48. mr + nru + prdus
  49. +nt y
  50. utyus + ptydy
  51. mus dus
  52. Hoc artificium late porrigitur, magnique est usus
  53. non nisi per aequationes ordinarias quaeruntur
  54. f9 + ggy + hadus + K9yy+ lqydy teu dydus
  55. FB + 9βy + +K Byy + l Bydy + eBdydy ubi in bsdu substituiuu
  56. -pip 6 h sen
  57. et W id = eque cCH P): p W = e (9+B): p + = K G+ B): n
  58. lydu
  59. + nwoydus + ropdydus
  60. Valorem- m.B
  61. B K (9+ B) + e (9+ () = l (9+ B) habetur Q per fit PH + n e = l, adeoque habetur p: n
  62. sit 4 = per t mo, . h
  63. ab solute percysich q = pr + em (4+ β): p seu m = phq = ppY, : e (4+ ()
  64. per y fit rem per y fit m = OA+ B) Lh hB~ - nY, . t ubi a est coguita n: p
  65. quos duos valoas aequabimus, fiet b h H tqp. et pp - eg qu Y C) - Ct ae (11 () et (1 ) a p
  66. ubi faciendo eg qu (qB) et (3~ (G+B) - a seu o+B = h Ba: g seu g ha9
  67. fiet 1. 1) seu 9. B - N h: g - , seu B = 84: v b- 9 et q p l f9. teh-9G
  68. et htq- rtp = - er (4+ B) , seu p = ht q + er(quB irt seu ht (k - C)
  69. et ex y fit ne
  70. Ex i fit m m = sp. fghas ( h . 5) p = mti X D4 (. oh. 5) s xp ~ f har que vtr 9) - ham 946, e b. 5)- a ppo: t
  71. seu pht 4 p- tq et + erolla : et compendio P= 4V = 4 r; +
  72. ubi pro p ponendo Nalorem iaventum evamoscit qy era nescit 4 et fit
  73. et in = f(gho (, ovh -9),: h9(4) (. arh. 9) = Gha q (, vh ∞) hgqu (., eet ns)
  74. et evanescit g et hajus aequationis ope fit t 2) (, ( + A) - ...) = ( = o 4(p + Z)
  75. es habebitur 1 vel F imo oblitus sum C jam supra inventum.
  76. Explicudo t e m = 9 C9+ () - h C arp = va ppY, : K (4+ B), quem valorem priortque aequindo qui erat phqus - ppY, : e Cq+ B)
  77. poterit utrinque di vide per p: (9+B) et filevg (9+ B) + eh B0 - V V pY = Khq = KpY et habetur
  78. p = e g (9+B) + etr βaa = Kh4, :, ea vr = KY. Ex i fit _ emp + ntB = fP (9+ 3)
  79. seu m = fp (9+B): rp + hβ, quemo valorem aequando primo pha - pPF, : CCG+B), pervenitur ad pP,
  80. et fiet esqu(qet et fiet e ( que) = hrgp + hhB9 - rip hBp, et faciendo esfed lt q es qu( 41B) th eq
  81. fiet hrq rep p. hrq r p= hrqpbr h(4 C): Y, sed hura ipsius P
  82. tu esoer
  83. ralum imentus veti expiores
  84. aequata
  85. qecuu incentur e) qordtatie nes mito quon
  86. id impedini possit. itaque putorem succed ere

Cite

Leibniz-Handschriften zur Mathematik LH 35, 13, 2c, fol. 95v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068199:0190?run=74