Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 3r
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: 0.88.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 7v); this page is its right half.
The machine reads it as
- qua Quaentur (dx V(XX +bXx + ac). sit xe fiat () Sydx
- fiat y -(x + Z et XX + bX + ac = (β3tio) XX + 2x Z + Z2 Unde erit
- X = (4to,, Z2 ac, 8 b - 2Z et dx = (5to) 2 du (:, l- 22) + (22 ac, X4 ( (b. 22)).
- et 9 = 22- 4c + bZ - 27Z, :, b - 2Z seu y - ∞t), -ac - 22, :, b -27
- et denique ydz erit (mo), = 2d Z(, qu eb- 22)) acZ - (3 0 aacc
- b- 22
- contrahendi causa, faciamus ) b- 2Z = 2B, fiet dque seu eque - v
- et ZL ib V geosguo) Z= 2V et (10 mo) Z dc t V + : b
- Et ex aeq. Ellisse et
- Quaeritur se
- si quaeratur dx x + bx +ac) reddendo extrahibile quod sub oinculus
- est per extractionem ipsius X, non comprehendemus casum ellipseos
- vel circuli, nisi interventu imaginariarum multiplicando scilicet quod
- provenit per Y-1, idque facere sane curiosae disquisitionis erit, nunc
- ut hoc evitemus scribatur (ayB, faxSex VabXX + aa Ex+ a f) ubi
- drimo)
- video duplicem rationem occurrere, unum assumendo ad obtinendam
- extrahibilitatem, unam si destruatur bxx quod f si b sit affirmativa;
- alteram si destruatur af quod fietis ipsa f sit affirmativa. sed
- potrst
- vellem quod si utraque sit asfirmativa adhiberi etiam u alterntia potest
- via, sed si nentra riffirmativa sit non procedit extrahibilitas nisi
- praevia trans formatiore. Quam ut itaque ad ad calculum generale
- habendum oporteret facere transformationem etiam in generali formuta
- Sed nunc utamur eo modo quo tollitur a s. It aq
- sit ergo 3ge (ado) gy 9 f2di)-9
- pro ae f scribamus aagg, et fiet
- (primo) sagdx = Sdx Y (abXX + aacx + aag9) et 2d0 frat
- Caaque
- (2d0) 3)= GCay = X Z rg, unde (3tio) abxx +aue Z tangus a ze rng t
- unde (3tio) abxx + aa CX + aagg = X XZZ+ 2agXZ + aa gg,
- et (4to) x = 2agZ - aac, : ab = Z, et y = 2a97Z aa c Z + aabg a92 27
- ab -22 seu (5t0) ag = agZZ - aa cZ + aabg,: ab Z2, Et dx
- Et (510) Et dx = dZ, rag (: ab - Z2) 1 (2agZ- aac, ∞:, qu (ab - 22)) seu
- (7mo) dx = 2dZ(:, qu (ab - 22)), aabg = a9ZZ + (2) a9ZZ - aa cZ. Et
- tandem (880) (aydx = 2s, dx, qu (a972- aa cZ F aabus) : cub (ab 22)- quae
- aequatio rationalis evolvi potest, modo explicato a me explicato in
- sit Sed Nunc tentamus et alteram rationem, et pro abxx
- actis ejuditorum
- scribumus Hxx, nam video calculum ita minus assurgere. CC
- et sit mimo) sydx = Sdx A(XX + bx + aC) unde si pro XX stet - ZE, oporlabit
- pro X substituere ZY- 1. fiat (2d0) y = x +Z, unde (3tro) XX + bx + ac
- XX + 2XZ +ZZ seu (4to) X = Z7 -ac, :, b - 2Z compendii causa pro
- fiat (5to) b - 27 = - 2v seu et pro b fint 2f (6to) b = 2f, et habebimus
- (mo) Z = v + f et (8n0) x = v0 + 250+ 5f - ac,: - 2V, et (q y - vv + 2fv + ff
- . fiat a 1G. = ac - 20V = 2vf, : - 2V seu (9n0) y = vV + aC, B, : 2V et (uma) per
- itt compendium faciendo (10mo) ac- f = ag, fiet, X = ag - vv- 2fV, - 2V
- slotoro et = (12 mo) Ry = a9 + vV,: 2V, vel (13t0) 2X = ag ) ag(:V) - v- 2f
- l
- t1 et
- et (14to) 2y = ag (.V) +V, et 2x (15to) 2dx = dv, _ ag (vo) t
- 66t0)- 4ydx = ex do ag (.) + v trag (.v) + ag (L1) seu donique
- (ymol ydx ed
- rag(VV) tnagu(: V4) et si ab sit
- rit (1800) ve=hato, fliet (19no) ydx =ad, 129 +d
- aduq si hiaec ad Evcndum abplicentur ant ellipsin
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 3r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0005?run=74