Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 311r
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: 0.78.
Original at the GWLB · Page image · Annotations (IIIF) · Download text
The same scan as fol. 313v (00068196:0622), where its text is given.
The machine reads it as
- Hic a ve
- Q bihi per X; a y in differentioli non post
- potest simul tolli X, et a, nilis sit Z= mX + na + 51Z squi
- Mxa na = valori per B y, Z
- videamus an possit inveniri slere er Exemplum, ubi Z- valori
- ubi Z= vatori per H, X, a et quaerendo differentialem, ac
- Ope ejus tollendo X simul connescat a. Nempe
- Z= valori per y14 a Ergo X: a = valori per Hoc rgitur
- fieri potest, si ponatur X: a = y: Q ita erom ex = a
- ex idque dxia = d ytque
- aaaxxtyy- dy
- X7 Ydx
- sit a G dgrus x dy: yax = _ valori per y, X, a
- Sumatur GB om aequatio inter X, B, y, X, a, Z, tatis
- ut tram x et a servans leges homogeneorum, in qua etiam y et a
- solae inter se servent legem homogeneorum. Siet y: a= valori per z: X
- ergo dy: a = valori per de: dx , Z. X. Ergo dy: y = valori p 1 x es Z.
- sit aqu. apty A y
- agao
- ae qu propo ita
- y si ergo sat gaxedys=
- ili Ga X: 4 sutratur ydx: du = 8
- et absit 8 y: a=
- le
- A
- K
- Sumatru pursus y: a = valorip. e
- dlela
- pinprementalem
- val. per P. X = valori per v: X jam per differentialem
- aequationis 3, fit dy: a = valori per dv: dx, v:x Ergo
- (5) alter
- er ae 1. 3 et 5 sit dy: y = valori per dx: dx, v: X
- per
- 6 et
- jam per aq. 1. et dy: y = dx: ergo fi x div. per vabr do.
- Aor (St
- fit = dx divis per alteram valorem ex de, dv: dx, 8: X; jam ope
- 0g. 4 et 8 collatur , et fiter valor et fiet scu ho- AX. 2
- valorper v: X ((g. 3) nl pl. in X = dx diuis. per alterum val. ex d v: dx, v: X
- id est fit ex du: _X = val. per vex sine interventu ipsius a, seu constantis
- ergo solubilis aequatio per quadraturis. Gentemus in exempeo, sit
- 3:a + d. x seu yx +Pa = ax seu jamas- A 45
- a jam 1y9 =LXy seu a y: dy Ergues 2 13 fit yxty + adxY extus
- seumus seu dy: ex Fya: aX Xy, quae aequalo reduretur ad quodraturas
- essuratur a B:x siet v: x1- D. jam perdif. 44. 6. fit dy: a= vdX XB, ZX
- rio ayin ieu uX dx: . Ger aq. Eseu _ Rs: p.X) - v xin XX, sebit
- a0 qu vex aercndiatis e
- ingens compendium pro
- nera liibus
- aequationibusad Mechodum anque
- tiam javerscem. Mhullucianu
- sit dy: ex = v ( sit jam aolat no
- aequatul) inter v. y. X
- Moto hacter
- me excogitato sumitur aequatio generalis inter X et y
- Et hujus differentialis dat Y X. V: X. 9 quum substitua
- ita habetur v ratis abiter vul cui valo
- substitutus in aeq. 2. reddere debet aeque, 3
- quid si sic Aequationis rpperatu
- 5 Ieu dationis e smplicur
- differentialis erit eg. (4). Sumatur alia
- differentialis AB
- D = X. .y: X.. y arbitaria; ujus ope dab
- B) ~ 1
- e
- iteram de puremplicter, duas to aequando
- similles
- nos valores do aequando et dabitur aeg. 19
- ia
- X Y. V dy: ex ubi follendo ly. Ex
- per V sit eq. (10dm qua solum p y. v. quae
- et ita e illud
- dbet coincidere cum eg. 5.
- est egnerium quod arbitariae assumta
- ad omblas polentias littoleunta
- _ V = G a +by+ Cy etc. posito a ex b, c, daneo
- fit dv= ada + b ly + y db + 2c y ly+ y de erc seu
- do= da + ydb Ly Ac + eu G 1 1bv + 2C70+ 3Cy v
- essumatur v l+ mu +n s etc py eu fiet
- v2 1l= yamy du et alvtmBL cu Et
- equando aos oatore do ex eg. 2et 5 fiet
- e
- tua
- a + db + 5dc etc. c it a 24) e + 3y p C_ V abus quam
- e
- e 08 aqy eu
- ibet
- s at al Pa si 11 2.
- aa
- n
- a
- ul oer
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 311r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0617?run=74