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# Title: Leibniz-Handschriften zur Mathematik LH 35, 6, 6
# Folio 42r, page id 00068051:0083
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a = 2C XX dy ray ax = a dx sit X: a = aldz. 62 et g. a = addque: dv.  sitque 1015 2
fiet aX: a ractaque: d
et dy: a. 2a dd dv: dv3. Ergo dy: dx = ddv +Z:, ddz dv.
et ep og. 1 per 2, 3, 7 est ddv dz: ddque do  in a ddque: q f addque: v =. 1
2 aeq. 1 fit XX: aa dy: dx + y: a = 1
An sic X: a =  dy: 4x et y: a = ddz: ddv. sed ita ibitur ad dudv, do, do
sed ita non collitur a
X: a =  v, Z et g: a = dv. dZ sed ilarbitur ad ddv, Lv, v
An forte Ac reducta aequatione ad
Anforte sic ad sint co. p, dz, 5dz: p 11) et subtato posito daqe 0, et
sublata differentiasido ipsa saz: P, habebibitur Co, p, deo, dp, dque, ddeo, de p, dez 
quantilas multiplicans ddeo, sit aq. 0 ham siet eq hb et divelletur aeq. 2
in duas unam in qua co, p, deo, dp. ddp, de alteram in qua Wo, p, ded, ax, due
si ponamus duz =0.
quod si ponamus ddco = 0 et divellamus aeq in duas
et ita ut evanescat dap, habebimus aqu duas et divhhabetimus
ae quin qua erunt cd, p, dco, dp, de, ddque alteramtin qua C, p, deo, dp, 1Z
sed differentiando aeg. 4, h per 59(7. L. habebimus aequ ( in qua co, p, deo, dp, dap t
daque, quam ope et ope 5q9ue. 34 5 tolletur cd et p, et habebitur aeq. 6) in
qua dco, dp, Ap, d2 adz, quae est quasi differentialis ordinaria; sicet biversa
a priore: non tamen melior
et affuuntur
qui si sit aequ. 1) co, p, deo, dx dE ed daz dax, aduo
assumatur aeq co, p, deo, dp d2 daque dap, sdleo deducta ex firimnta
oerentiali constante deniue divellatur acit in duas quarm ambabus ubsit
adeo, quam purar (A(3)2 Htnct co, p, deo, dp, dZ, posterior co, p, aco, ap dap, to
diferentietur aeq 3 habelitur aeg. (5) continens ce, p, deo, dp, de, ddeo ade lu
hhabemr aequ. 3, 45, sed nit lacraram
An sic Aequalio () ex co, P, dco, dp, dZ dde ddp, ddeo.
dividatur in duas qarentes ddco nempe aeg. (2) erit ex
Cd, P, ded; ap, du; et exque (3) ex co, P, deo, dp, 43, ddzu, dap.
assumatur formula constans et co, P, d dp, dz quam differentando
habebitur aeq. (4) in qua deo, d co, p, deo, dp, dZ, ddZ, dd p. sed nec
sic lucramur
s sic bene. sit aeg.
(2
Sic bene  sit aeg. 1) inter X, y, dx, dys, a.
sit x. a = lo.Z
et y: a= fAZ: p follatur. Et ex. 1, 2, 3, fint ae 14) in qua erunt
dea co, Z P, dz, deo sdz.: p, ponatur  divellatur in
duas quam utraque non habeat Saz: p, quod fieri pt si saz. p seu
:a non assuigit altia simplicem valorem; et in un ta in una aeque
et6
erit dz: deo c0, Z ip, in altera itidem, quarum ope tollendo p
habebitur aequ. (7) inter se, Z p in qua C0, Z, deo, du
Sin dz. p assurgit ad quadratum; adhibenda erunt literae
plures, co7, v, prox: a, et (dZ: p pro y: a, inde habebitur
aequ, in qua tollendo tam simplicem gradum, quam quadraliam
habebuntur tres aequ. quam quaelibet continebit, peo, Z, v, deo, dist
ax- ex
si C=- 2