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# Title: LBr. 695 · Oldenburg
# Folio 52v, page id DE-611-HS-860722:0104
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diversis
Quantitatum ex defferentibus in definitis in se invicem ductis factarum
ut.
aequatio
et Lyxp2y + V x
d yx. erit   ydx + 8 x dy.
Dyx +
Hinc si
+gyx+ fxXer
a + by +CX + (y + fX + dyX M 10. statim habetur
tangens curvae ad quam est ista aequatio. Nam ponendo A, Bp y.
et A2B Y y + dy. (silicet quia
seu 1cd.
B2Bp dy)
seueD
itemque ponendo
1B16) X et 2B2C+ X + dX (scilicet. quia 2CDp, dx) et
quia eadem aequatu exprimit quoque relationem inter A2B et 2b2C
quae eam exprimebat inter AcB, et 1B, C, hunc in aquatione
illa pro y et x substituendo y + ay et x + ax. fiet:
a + by + CX + cyx + e y
+ fX
+9Vx + hyx
bdy + c dx + ayax + e ydy +2fXaX + rgxydys + 2hXy AX
+ axdy
a
+a
9y dx +hx dus
+ d dxdus + eaus +f dx tgdy X +hdx
+29 dy) dx +  Exdxdus
ubi abjectis illis quae sunt supra primam lineam quippe nihito aequalibus
per aequationem praecedentem, et abjectis illis quae sunt infra
secundam, quia in illis duae indifinitae parvae in se invicem dicuntur,
hinc restabit tantum aequatio haec.
b dy + cdX + by dx
b xdys
e.
0 quicquid sclicet reperitur
inter lineam primam et secundam, et mutata aequatione
in rationem seu analogiam, fiet
idest
∞-dy
quia
c
-dy.
ex 
C + dy + 25X +gy + 2hXy ec
b + dx +2ey +29xy + h X ds
= 1B2B seu - 1CD
seu
AD2C
vid
FiB) erii c+ dy hc - T. B
d B1C
b + dx ex B
quod coincidit cum regula Plusiana, ostenditque eam statim occurrere hanc