Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 83r
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The machine reads it as
- Ad Act. lips. januar. 1691. pag. 15
- Ver + arryu - 8ry + 4u dy quaeritur ut habantur
- longitudo curvae quae fit si axis parabolae convolvatur in
- pariboa
- perpheriam circuli, et ordinalae sumantur in comvergendubus ad
- radis a circulo ad centrum gust)
- xrk +4rryy -8ry + 4y = veu + 2rl co 2y. Pr y + coco. 4yy. Fy
- seu 2y. r-y = + 2rlco + coc0. 29. r- y et seu - 2yy + 2ry = f2r100 (-2059y + ory
- seu gy +2Y - 2e0coY y = + 2rla seu yy - ryH +rr = rcoco- rr + 4rico
- Fcoc - 2
- quae quantitas
- 2CdCd 2
- ercoco -er qarlcd
- 4c0c0 - 4
- 401-4
- aequanda quadrato. Sed hoc panto
- a
- 22
- diffieilius
- rC sit 29. ruy = re fiet Al + +AeC =Z. quaeritur szdy vel fy dzue
- est autem ( 2yr - 2yy = re Ergo 2dy -2ydy = rde et dy = rde : 2r- y
- vy =yY +: r = rr- 2re. seu C88C =r - y = , Vrr. 2re. seu y = r - Vrr- 2re,: 2
- et dy = Yde et 2Y - 29 = 2Y - Y + (rr - 2YV = Y+ Srr- Ere
- ergo fit Zdy = r Su+ ee de : r+ Srr-2re, seu = rriutee- r Utee. Trrrre
- tantum ergo opus foret facere Su+ ee. rr-2re a qualem qua
- + 2rC
- faciendo rr = 2re = vD. fiet C = _ rr - vV,: 2Y. et jam ll+ F - vV + V
- 2
- equantus quadralo faciamus WV: 2Y = W fiet LY = W = C, et ee = Lrr - rW + Wio
- et U + : rr - rW + Wveo = quadrato U+ er + W V sU+= rr + WW (1
- seu =r + W = 2 b M+ Zir + W (VIP
- seu W = 21 M+ = 1r +Y,: B
- quae quantitas rorsus aequanda quadrato et a m_ + n9,:, 1+V
- fiet sit 2. a + Lir =h, fitt. hI +Y = ns v + 2mn V8+ nn88
- el si m = 0 fiet L + hr +he Frib
- I2 +n +X +h
- d14 1p
- 1+ V
- ungg nnv 00. seu
- V = = un L hr sed ita extractione
- centando reditur ad priora, et radio extrahenta ex quantitate
- in qua est D et
- ut supra ex alia ubi ovet vi
- praestat ergo solum radicem quaerere ex Urr -Ellre +Carree- 2re
- Urr + 2res L ecEE
- fit - Ellr + rre = 27CC, = 2lr e∞ + exr
- sit Ur + ille ra + 3 (C3
- ubi redit difficultas
- 9+ 3599 +c
- nisi in casiba specialobuss sict
- Sed nec sic progredi lice
- u ut spleciales tamen casus namto
- pro nmmris rationatibus refecriri possunt, ut in ag.(t Faciendo nne = hr, seu
- n Thr (uam irrationales in ipsis cognitis non curo) fet h + h4 fr = 4 nn
- et datur casu speciali
Cite
Leibniz-Handschriften zur Mathematik LH 35, 6, 4, fol. 83r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068049:0165?run=73