Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 42r
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: 0.86.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 41v); this page is its right half.
The machine reads it as
- traestat ergo retinere gereralitatem aquationis D faceere
- bb + 11. H + 31. 31 + 2.7131 = 4 a (11+31) + 1131 - (11+ 31) B, 11 1135,-
- 49aa
- aquandum quadrato s ubi seu bb - F - 2 (11+ 5131) +6. 1131 -B b (1139
- 36aa 3a
- seu (1 -- 3t - qu - 3 qu (1 - 31) = b (11431) + bb - 12 fa quod
- 35ga
- aequandum quadrato. sed idem licet aequare nihilo. Quo facto
- = in duas divellemus aequationes, unam -2 (1 - 31) + 3 bb ee, seu
- 11 -31 = +bria alteram. 3 bbee - b (11+31) + bb
- a a
- seu 27 27 (27 ee + 1) bb - 12 a5-
- 36aa
- 4 aa
- 3taa ha
- (11 +31) ubi e est arbi
- taria
- et n ita solutio habetur rationalis, modo calculus sit probus. Ubi
- e arbilaria ita assumi pt, ut numeri fiant quam minimi
- 2 ex. g. si e esset 3 foret 11 - 31 = + b: 3a et 11+ 31 = 6 bb - 3af. 2
- 9ab
- et 2. 1 = + 3bb + 2bb- 6af. subi si + = - fiet 1 = - bb - 6af
- et et 6af = 3bb -6ac e Ergo 1 = - +bb +, 6ac
- et 1(- BR = 31 = 11 +
- 2.9ab
- 2.9 ab seu 1 = = 2bb + 3ac
- da Ergo 31 = - 2bb + 3ac + 3bb = bb + 3a5 -3
- Et 21 = 114 31 - ha = 2bac - bb - 3 bb - 6ac - 4bb
- itaque 11 = 3aC- 2bb 21 = bac 4bb
- gab
- gab
- ab
- gab
- 31 = 3ac L bb 9ab
- at vad
- 10 = 20 = 30 = 1
- attimativa, incideretur
- in imaginarias quaener quae cujus que haberetur 11- 31
- +0
- et huic emtando posset fier. 3 qu (l-3) - 12fa + b. aequari 0)
- 36aa
- et restaret - b (11+31 + bb
- - b.. -0 ita b non inpedietur
- vaaem expo divilo, nominatorem in valore ipsius 11+3)
- 36aa
- pplicatione facta ad Ellipsia et Hyperbolam repo videbinus quae
- sit conicae contricae aequatio 2aX + (a: L) XX = yy sit erit adx +(a:b) Xdxcydus
- sumtio optima
- seu dy: dx = a + A: b) X, :y et dydu: dxdx = aa + 2(a a : b) X + (a a 1bb) XX, :yy
- et dydy + dx dx = aa + 2(aa : b) x + (a a : bb) XX + yy,: yy, seu fiet
- aa + 2(ac: b) + (aa: bb) XX + 2aX + (a: bGXX , per Z ax + (a cbx. fiat
- aa tatb: V)ju :gu + X = Z + C, et fiet 2ax + (a: b XX;
- seu aa + (a rbs: bY
- (a:6) ZZ + 2 (a: b) cZ + (:b) cc + 2aZ + 2ac s, destinantur terminus in quo
- simplex Z, et fiet 2(a : b) C + 2a = 0 seu C = - b adeoque X = Z - b et fiet
- a: b)Z3 + ab = 2ab = gy seu (a : b) 33 - a b = yy seu Z2- bb = b yy
- Ergo tandem dydy +dedx,: deax= Caa) B aa) 8 ab H(a a. bb) ra : b)) ZZ.: ( B) (a: 6) 2Z - a b
- at b, 5b) . L) = (a + b a : b1Z3 - ab,: (a: b) ZZ - ab
- b: a). et dzdz: dydus = (yy. Z2) bb
- et dzdz + dydy dy dy-(99 4 (bb: a4), + Z2,: , et fit ((bb : aa) + (b = a )) 2y + bb,: (b. a) 12 + bb
- ex eodem valore ipsius aZ. ay dy: dz habuissemus dydu +dzdque: d dzdzue hoc modo, examinis causa
- dy: dzue -Z. 9)(a: b) aydys: dz dze - (27: 9y) (ad: bb) et aydy+ dz dz. : dedZ = 23 (ac .b6) + yy,: yy, seu
- (aa: bb) +la: b1) ZZ = ab: (a: b) 22 - ab, ut ante
- Mutemus d et in Y, et b in g. quoniam ipsus literas a et bsupra aliter sumsimus, et
- TCi Fertarquu +rY9q (r; et q)
- reducta re ad atque ordinata ad scopum nostrum fiet
- (est atr4q2Z + 1r44 4 C4, r + 4)
- = dy -
- yy +rq, Ver:, r+4)
- itaque nitaque ut irrationalis ducta in dZ vel altera ducta in du, divellatur in irrationales simpliciores Methodus
- -94 (4, r+
- lys dus + de d 2) = c
- Nota in hllipsi e semper majus quamr, circulo excepto, ubi aequantu
- C in priore semper est affirmativa, in posteribre est affirtua
- acaso ettes pepr in ces ae tur e su i put e aste
- n Ellissi lonst n aserntra rationali destrui bZZ vel b0
- ZZ (b, aarab) 3, Z
- hastenus explicata
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 2b, fol. 42r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068198:0083?run=74