Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 411r
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: 0.83.
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The same scan as fol. 410v (00068196:0816), where its text is given.
The machine reads it as
- ses explicabit et hunc sngitu sempulum
- et fiet cbcod0
- (13)
- opinor tollet. Si jam semel habemus arquationem ob XaV, 1+ C + ma =0.
- 148
- ob vdco, - 1 + fa + hb = 02
- 6)
- i differentiali carentem, vel ummabilem ob Xdco, a 1+5 + mb = 0. al codv, -1 + eb+ (a =0d =
- vel summabilem ea
- seu
- linan
- in quasartum unt
- vel sactem differentialem poram
- etemgatam
- poterimus in ea tollere supermlnerariam literam
- dae
- ope aequationis assumtae nempe
- quod si aequatio differentialis non sit simplex sed in ea
- ex du ascendant ad quadrati planum, sen ad secundus
- gratum poterit multiplicatione per novas
- Efferentialies alia conflari, in qua priori addita tollantur
- hiterminui. Ut proinde sutem reductionem diferen-
- tialjum caelerarum ad rationales evitari posse.
- Quod iffinet ad differentio differentiales et
- puius reducendae ad differentiales, et hae demum
- (2
- ad summabiles vel summatrices.
- pro y scribatur y= v +c
- 1
- Xdy + X dx = y dy vdco
- fiet Xdv +Xax= vdv codx + codco
- assumatur aequatio nova: aD + bc0 + X 0 cujus differentialis
- xde
- aeda 1 b deo + dx v0 mulsiplicunda per ex, fV, g0o, et fiet
- multiplicanda per Cdv, fded, odx,, et fiet
- 0
- (20
- ea vdo + eb codv +CX du4
- fa vdco + f b codeo + f X deo
- ga vdx + 9bco dx + gX dx
- sursus ipsius aequationis 4 differentialis a dv + bdco +
- multiplicetur per h v, 100, mx, et fiet
- 0
- ha v do + hb vaco + hv. dx
- La C0dv + l b codco + l co dx0
- M a X de + m b X deo + m X dx =0
- Si jam ad aequationem 3 addantur aequatio nes 5, 6,79
- es ex omnibus composita aequatio 12 p
- G1
- ob vaX, ga + h 2 o lo, gb + l = 0 X
- ta
- ea quae ut
- ernt omnes.
- reddatur ctablis sugmabilis tolci poterunt
- non suam
- fiet e - 1 - ma f = - 1 - mb h-
- (22)
- - gb
- lde
- quibus quatuor valoribus substitutis in.
- aequationibus 1F et 16 fiet:
- -1 - a -amb - gab 20
- (24)
- = 1 - b - bma - gab =
- (26)
- et (e 1+ a + maa + gaa =0
- ublatis jam in aequatione 12, terminis, in quibus differentatis
- et posito m = -g. fiet a= - 1
- iemas non suae restutrit
- po
- em, (quia sedv= Lvd, et iti in caeteri
- (27)
- compinatur
- -1 vV -1, coCd + 1 XX Z 0.
- d
- + ea
- +ha.:
- +f
- +la
- ex
- seu per aequationes 25, 27, 28, fiet
- 2)C
- =1 VD - ∞AdC + KR 0
- e. F.
- +9
- m
- 29..
- unde per aequationes 19 20 21, 22, fiet:d
- Th: - l
- =1 vD (1 coco + XX2 sed haec explicatio non
- +
- +).
- =M .. M
- -
- e
- procedit, destruuntur enim ut
- tam V, quam co
- Ergo non procedit pot setro assumta in aegus. 27. 28.
- =g.
- q.
- Ergo ex aequ. 26 fiet m= 1 + a4 gaa,: aa
- 3
- t valores ex aequationibus 19, 20, 21,22, 32. substitui
- et ex ea fiet:
- debent in aequatione 29
- -1 vo L1 100o + 1 XX sed ita oritur idem alsurdm
- quod in aeq. 31. nam
- destruuntur v et co.
- +g
- .
- +m.
- non ergo licet destruere, hoc quidem calculo) terminos
- ma..
- maa.
- gaa
- omnes, sed ut generalius procedamus praestabit aequa
- 1gaa
- tionem 12 comparare cuma, quatione gneral
- limabili ejusdem gradus. Quod si ne dolat
- 2
- ax i
- v qco +r xD+FXO+ Wvi=
- auisio aridd val vervinti taduo teia uid st
- Ergo a
Cite
Leibniz-Handschriften zur Mathematik LH 35, 13, 1, fol. 411r. Machine transcription, not an edition: Leibniz Legible (model FoNDUE-GD_v2_ft_Leibniz, run 74). https://leibnizlegible.com/page/00068196:0817?run=74