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# Title: Leibniz-Handschriften zur Mathematik LH 35, 7, 2
# Folio 15r, page id 00068074:0029
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(15
jam ex G est 2y ay = adeo + 2Bdx = 2X. Ergo fit
16
du2 = adco + bdx - 2x dx: c3a - b B F 26X - XX
N
fit rasiedi et ddae de 1
Ergo
a deo L 2a p - 2x dxdeo + b - Ex dx 2 + co A - bb + 26x ∞xY du
ca - bb + 2bX = XX
quae quantilas est constans assumta. Sed hoc prolixius
um  quia dxrdus = constanti pErgo fit E ax ddx = - dus ddus
sed ila non possumus rursus, collere dus ilaque nihil proficimus
hac via. sit b - x = Y. fietque. Idque = ydy = rdr, : Lyy +rr
Ei
et  quia ex = = et. Ergo ex 3 fiet: dr + sy VygArr: ydy-rar = Ya. B. Y: a
quae est differentialis, ad priolema solvendum construendam
23
sit  Y:a = SddZ: dque et y: a =) ddz: dv   G 21
24Y
 sil dr de dy: dr= dz: du Exaequesit:
Si+ dyidr Syg:0a + tr: da: y: a dy: dr - Y: a = Sb: a =r: a
e
e
se +
(36)
1+ du: dr. yy:aa +rr: aa (: b: a - r:a = y: a dy: dr tr: a 2y Y du
a a dr
et fit 1+ dz. dv. (adz: dv + (4dZ. dZ: b. a = Sddz 1Z = (aag.tri dF +  - 2sa, sab
ey du do
(2)
cunqus aeq. ope tobtendo (adZ. Av ex aeq. 23. habeheturG: a
+Z L
in d24
per Sadz: du dec dz: d Ex aeq. 27 tollatur sadzu: di
differentiando; fiet aeq. (28) in qua erunt, saaz: du, do, dz, dav 
pingatur de =ddz: du de et dde =0 fiet aeq.
19)
nova, (tolleado de ex aeg. 29. differentiamto) nempeaeue 31
in qua erunt ddze. dv, daz. et s. Idz: du cujus ope
collendo (ddZ: du ex aq. 28, fiet aeq. (32) in qua
erunt du, dz, ddo daz
adeoque habetur
lal et
do ope ipsius dy. quadratorie. cajus ep
ejus ope tollendo dv ex aequ(27) habebitur aeg. (33,
in qua dabitur qua per
(ddz: dus, neque enim
aliquid aliud inter venive potest si non intervenit a.
Ubi si tolli posset (adZ: dZ per aeq. 33 et 22, haretur
relatio inter X: a et y: a. eaque ordinaria. Sed si
fieri potest, ut it aeq. 32, adeoque et 33 non habeatur dv per
e
solam sed7: dus et dZ. sed ut in terveniat aliquid aliud tran-
scendens ut verb. gr. etiam Cadv: . aut aliud. item ut
transeatur ad exponentiales. Ita redire poterit a, nullo
Jam damno
177
du tdy