Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 301r
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. 300v); this page is its right half.
The machine reads it as
- possumus eriam assumere, ut Z non sit dy. dx sed ait aliquid pralica
- ut 1nA + aX + by = CX dycdx + C y dy: ax e sit Z= ex t ey dus: ax
- ser dy = _ 2dx: Cx+ ey et. ed fiet h + ax + by Z Z adeaque fiet
- a dx + b dy = aZ et per 3. fit x a Cx + ey dx + b7dx = ext ey dque
- pam
- ex 0q. 4 est y - Z. b a h. b = a X b. Ergo sit a cx + a Z. b dx - aCh: Cax + a CX: b x
- + b7 dx = CX aZ + a CZ. bdq = a eh: C du + a a ex: b dque sed uit hinc lucram
- Tale quid in mentem verit sit aequata, vg. h + ax = ex dyndx t Cy ay: du
- h + ax + bg = CX dy: dx + eydy: dx seu ax + b9 2. ex dyidx + eydys: dx h
- fiat 7 =, Cx dyodx + eydiy: dx = h,: X. fiet ax + by = XZ, adeoque
- E sit seu a+ bgia = Z seu a + bD = Z posito v = y: X
- a X + by =ZX seu adx + bdu = ZdX + X +Z
- a x abus (xy + Z fit adx + bdys = xay 1B dx + d2
- seu ex aeg. 1. est y = ax = Z, : X - b ergo fit a dx + bilus, x - b = X dus-
- a ex eb du dq = b - _ dus X. X- b = aX - Z +2
- aX _ Cd ax C, Z Z) + Z sit a p = Zdy 17 dZ + dq
- ax aby C+ 1 xy sit a E ZXy
- aial
- ax by = ZX7 CZ_ - a X + CZ - b y 20 L2) mX+ ny
- fit X = 6 = ny: m D HL -m ndus - m ydZ + ny de, = mon dx
- ubi proes substituendo et fit y umdx madus.
- et fit imax + mndus, ndque - maque = y
- et un dy + mnde,: maz- ndz = X
- et atbos valores substituendo in aeq. 2. siet
- mundus + mmndx = mmndx- mundus
- et ia tollantur moest evanescit et de
- sit mx + ny = h sit X = - ny: m + h: m et axmni
- et de nim ax = mndus = my dque + ny dque = hdZ
- Ergo y.= um ax + undus +hdZ,: n. - m aZ
- Et siciliter X = nm dy + nn dx + hdz : m =n dZ
- mundus +mun dx + nhaque = mmndx -. mundus - ulidque = tmaque - hndZ
- Ergo luis valores subitituendo in aej. 1. fiet
- quae rursus est identica. itaque nihil sic Cucramur, nec possumus collere simul velfis
- itaque aluid notificium at me utem venit, ubi praesens artificium ponendi
- A Z = dy. du comb et quaerendi 1y. combino cum alio attificio
- observatione, qua deprehendi semper posse aequationem esolvi quando differentialer
- 1od
- per se solae servent lomogenertateur.
- rno ad set aliqua constans vel plures primum
- solvi, quando X et y.
- sem per plures constantes
- pro b poncae possum Ba
- et X sint numeri sola vero
- edicemus ad no uinam sint enim a b icu
- et pro c ponere possimus X a. ala ab k sit β
- a sit linea. t Ergol egc. sit ergo 2 xi Et sit
- et sit aeq. (27 proposita, inter X. y. Z. a
- Huijus quorantur differentiales duae, (3) et (4); quas combinando cum ipsa 2, habebimus
- sit ergo BCC du = Zdx.
- duas oquationes (5) et (6) in quibus aberit a, jam ope aequationum 5 et b tollatur, sit a
- g et ope aq 1 tollatu et ope aeque 1 tollatur. dus. habebitur aq (9) in qua
- et x adcoque
- erant solum Z X de dx. servantibus legen homigenectum. es
- solibilis erit per quadraturas. sed quo verenda destinctiares restreipsa
- Tetnda sit L, Z te s L CxZ + C yZ fit hi CxZ
- Zdx = dy es h = exZ + eyZ ubi h es constans quae solu turbat homogenersolem namus z est
- ratio, et c atque e, sunt ut cumeri R fil CxdZ + CZdX + Cy dZ + C Zdy = 0 quae est sine R.
- varsus h: Z = X_ + ey. fit 2dZ. 22 = c dx + edu - - ex - ey, Z. Z
- habenus ergo duas aequatiores in quibus abest a in quibus tollendo du per aeg. 1. sit
- exaeg. 3 CX dZ F C Z dx + ey aque + eZ2 ax =0 et ex aeg. 6 fit ZCdX + CZ2d X. + Cx d2 + ey dq = 0
- 30
- 30.1
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 301r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0597?run=74