Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 1v
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: 0.80.
Original at the GWLB · Page image · Annotations (IIIF) · Download text
One image of two folio pages side by side, registered by the library under both labels (also fol. 2r); this page is its left half.
The machine reads it as
- timeo ne semper _ X et y siviul sublata secum tollant dax, ddus,
- quod ita videbimus qt hi quia abest a non possunt esse aliae quam hae quantitates
- y: XI, dy: dx, ddy: ddx, x ddu: x, patet autem tolli posse
- has duas quantitates yix, et xdax: d. residuis manentibus
- duabus dyidx, et ddy: ddx. Itaque spes adhuc manet
- sit exemplum: a )f1 X ax + uXdus : x quam differenta
- s
- ilo
- y ax
- bis
- fet: (+ 10 X dx ddx + 10 dx3 + 10 X dy adx Fro dy dx + 11 Xdx dai dxdeuxirdlus B
- y dys ady)
- - 10 X dx ddx
- Y dys ddy)
- dyd
- y axadys axa ydydax dis dx) exd
- 11 X dy dex
- = 11 Xdy ddx
- ydx day
- = 10 Xdx ddys
- ydya
- =UXdy idu
- ydxalx)
- Ubi tamen rursus tallu et sin video et mivor non posse tolli xe
- quia simul tellatur et dax, dayue. Videamus an non possit formula obtineni
- in qua sublatis ordinariis manere possint differentio. differentiales
- g. sit 1axd+ soq 10 dx, et vibio rem non posse obtineri, nisi assur
- gatur ad dax. verb. 10 Xddx + 10yddus + i 1 daus + 1 adx
- de
- dax
- day
- ax
- ayt
- et 12 dy + 12 F 20 haec reducta dabit: 10 X Ay adx ady + X dy au x apd exdbus.
- y) du dex ils ux d axady x
- Ax
- Sed simplicirem scribere possiumus.
- 12X dx dAx + 13 Xaxclus + 14 Xdy dex +15 y dx Ade +16 de ddx +17 de dly
- y ay day ydy dux yaxd xdy s di sar di alx
- +18 dx dydix + 19 dx dy ddus = 0
- tus axadus
- dy axdax
- V
- Geideaur ex quanam
- differentiata talis oriatur:
- X ex dux Xddx, dx et horum aequalibus
- sit scil. 20 dx + 21 X dx dux + 22 Xdi ddy +23 Xay dldx +24 X dy ddus + 25 Xali, b
- 2
- y du ddy ydi dex Yax adu yax ddx
- Scil. ex
- dyt
- linus difalis: D: x H 21 Suffecerit ad hic simplicur: X
- +
- P
- uus diferihalis: 2ode x + 2Xd a +2IX dx x erc. seo hic illud vitiem, quod Prodit dudx
- 62
- tu dau
- dvadus
- yay dd es y dis attus
- ideo ascuntitiam aequaveno 3 esse debere talem, in qua sit relatio
- inter . Co, deo, ddco. posito c dari utcunque ex X et y; ut
- COdda +30 deo = 0 vel codd Cddo do 430do
- vel dao + 30 Cd deo dded + 31 co ddo = 0
- vel deo + 30C dio ddo + 31 co do adco + Zt co ddco
- Et ata porro, et ut verbo dicam
- Et
- ponatur co ddeo -g fiet aeq. vel 9+ 30 vel ( + 309 +31, ve l9 430 131913
- Etc p.
- et ita porro, nec apparet quibus aliis modis assumi possit progressio
- deo
- Verum cd esse potest utcunque format. ex x et y. formemus rationaliter, integre
- homoeoptote sit Cd = +41X _ lfiet cd do hod= dco = 41 dx adgo - 41a
- ay
- a abcu deet hopsu
- Cd ddco 430 de = 41X ddx +a1. Xadus +, AY + 2. 30. 41 axau 20 Hoc si
- arrax multipliitur hoc per a dx + dy, et fint a Xdxdix etc. sed ita non assurmitur ad
- ydas
- y cdq
- unde tollendo xerus tollitur semulilila duus oportet ergo trasire ad ao, et t
- y dy ddy
- Verum Video jam quod omnes istae Hrypotheset ut 2 =40 codlo 2o
- vel ded + 30 codio Eldio 31 Cd aco, 20 et An porro hur non profunt, quia non pe tolli
- Ergo
- X et g, s quin simul tollatur daco Xdax +X
- disco redeundum ese ad pripum, motum maginae praecedentis, sublato pruum y, dende X et du
- in non ibsevari pommeontosis
- ady
Cite
Leibniz-Handschriften zur Mathematik LH 35, 6, 6, fol. 1v. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 73). https://leibnizlegible.com/page/00068051:0002?run=73