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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2c
# Folio 80r, page id 00068199:0159
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sib _vIx=  ft duc mx exdmet am= dtdum lv. vdx+ XX= Ado rax sik
sit aequatio X. Y. V (X. y. B = a. (X. y. ∞ unde fiet
differentialis primu
adus:
a X. y. D leg. a: X. y. ∞ = d. X. y. D: X. V. B. it
3
2
ust
jam aequalio X. Y. V = 0 cij cujus diffelentialis HM.
ua
d X. y. V = O ex aeg. 2. tollatur V ope aeq. 3, et dv ope v9. 4
va
et sola restabit aequatio inter X y. dx. dy. quae proinde
constrin poterit per 64 e3 aequediones 1 et 2.
Exemplo utamar. sit agua 
a sutvo et fiet
sit X+y+ V (xty) = a (Xyv). fet
loga. Xt y+B _axyd + Xvdy tyvax Pa - log. a XyV extdy+ dV
=Xty+p (qu) in dx + dy + dv (: X +y+V)
sit vi=aa et  vdy + ydv = 0 seu du = vdy: y seu
Hiuc tolli possunt _ et Av ex aey. 2.
 
dv2 eady: yy
pomimo sumam brevius, exempliu
= a (∞) fiet dyt du: y +v= bogdx+xdv
XX
sit v= aa :  et duZ-aa dy: yy. et habebimus;
 y+ D (X
ix
dy g au. gu fe dyXX - aa dx: yt aa: X XD = legB  24d: X
seu fiet dy X3 aax x= log. a  
dyr aadx = bga
seu, dy x+ = aux dx = log. , - 2aay X dx A- 2 a dx
itaque aequationem propositam differentialem impli–
catam: 2 dy XY = aa X dx 2aay xdx 2a dX
V + aa : X X) = num. C saa: X
nemo facile divinabit. endem generalius tertari possumt est eumna aperta
solvi posse per hanc.
L
sit aequalio
quadratrix ut y =  sna - XX dX
su = saa-xx dx videnmus au licut facere sua x 
Si
= 4. Y. V. S.F onuamta scili et relatione inter X et V e y videam
vil eamus an liceat mutare in Logarithmicam, nempe feri multiplicetur
uncumuo ut nen alter aequalio per iig et ner Aix et fief.
ponatur Iaa = XX = C  + 1: X is, et per
dy:  = cAX + dx: X seu log. y - log X = Scd sed nihaue
ninc