Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 364r
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: 0.85.
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One image of two folio pages side by side, registered by the library under both labels (also fol. 363v); this page is its right half.
The machine reads it as
- ga- do: dz X: a =sZ Z dy: ax 2bri Z S ddv dutratue: q datz
- y: a = d2. 10 _ x. a t (12Z sit los cotans fat dy: dx- 2 dq. tu bo
- Aanc aequaven dy: x= x: a + jgiaa ex periundi causa vertamus differentiando
- in aliam, ubisite du, dx ddus, dax, duo. six i fit deddu e- dytn, : du = dx: a + 2ydu: aa
- sit ydu yyddus = adco et sit ydu adeo et ergo ex 5g. 2 fit
- dx ddy - dy ddx, : dp= dx: a + 2 adeo: ad Rursus ex 3 fit g = adoidu quam
- differentrando fit: dy = - ddu a deo: dij. seu a - dy: Hydeo ddus. Ergo ex F et 6.
- collendo a fit du ddx-dxddys, dus dx + idio x deo ddus
- suod verum sed non profutum
- C. y: a. = dx dee cv: deo X: a = dv. deo (ddv: daque du
- dy: dx = a y: a = de + dz: deo x: a = (ddv + adque: dv
- dy: dx ~) du: deo Sit jam dy: dx 2 x: a + ygiaa. fiet:
- du: de = (ddv +daque: de + av. B dvodi: do, seu fiet
- d
- (51
- ddo : deo = dav idr + daz: d Ld: deo a ritcqu dive 2dvrd dav + 3∞: di
- sit deo. d dZ. da = dlv: ddque n sa ld Z: dq dut to
- lit deo = du dZ Sed ita sit non solum poterit tolli deo,, sed et dabitur
- Ax. a = actx: n ax duo
- Vlatio inter ax: du et ddv: ddz. bis, quod absum
- X: a = 4
- (12
- y: a = f8 a ddz: deo
- Yia = seaalaque Bduao,: decto xia = du F dz: dv
- dy: dx = a do daque - az ddv: ded du: d vddz- dzddv: du = do: deo
- y: a homogencmm atzide u si esset y:a = dZ: deo et X. a. Halaz: d = a
- et X. a - fdio daz. d2 - 46i
- et dy. dx = et X: a = 5a dax: dx deo
- Xia=a. x de: duidx d deo
- dique. adx
- X. a = _sdZ: duo a
- dy: 1x = dtque H a: qv
- (3
- x dy: dx = X: a + gyi aa tollendo e per differentiationem, fit:
- dxtlys = dys dex: dx 2 Ax: a + 2y dgs. aa fingamus dx:a + rydy: aa = ddx: dus
- imo non puto licere
- (adx ddus ∞ = dydix: dx = dy + ydlyrar = dec: a et fict ddx: a + vydllu. aa +rag. ac = a
- Sed ita non licebit simul tollere a y deo
- si villemus uti ag. 3. fieret xexu de dy ditus - dus dix = dx ddx
- dc. dy. y. x sit Z cblys: dys : dx =Z dly: = Z fit dux: dx = aZ 2
- log ex = log. E logZ ubi intrat (opinor) deo, nobis a non licet
- nos autem ex assumta aeq.3. nescio an possimus habere deo
- Ea est proporitionalis ipsi aa a deo: a = ddv, posito alo est
- Nante
- sit dy: dx L) X: 9 + xytgy, gaa
- dxAdus- dydex Xdy- ydx Xdys +y dx + 2ydy. fiat xdyaydx trydys = dae constanti
- a
- a
- et fiet: X ddy + dx dy + y ddx+ dxdy + 2y ddy + 2 dyt = 0
- Omnis calculus, ubi sublatis quoad y et du fractionibus
- fantum et irrationalitat et sablatis etiam rationalitatibus habetur
- tantum X et dx non xdx vel simile aliud, item XX et xdx, nhil aliud
- facile tractari d per series.
- si possent tolli illa conposita resemper
- idem est, si detur X, dx, ddx.
- educta ad simplicia pulcherrimm. set ae. g. aady aa = axdx = gy ax. HiC
- duo sunt termini sed non respondent aa sit dy constans, fiet ddy =0
- aa ddu a x adx + adx +2ydydx + 9y ddx =o gady: X = aadyolx; p et fiet
- =aadyodx: x = a ddx + isG: X ddx + dx X2 ydy: X = dx gydx: y
- seu aadus ax = a X dax + X yydax + 2 Xy d Xdy - yy dx2
- non dy: aA daz: Aco
- seu agdeo honisit
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 364r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0723?run=74