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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 18r, page id 00068198:0035
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Methodus Tangentium inversa excalculo.
rentampnitum subtile, sed iritum
proprietate 
 adx +fbx da AF quaeritur curva ex methodo
tangentium data verbi gratia sit BPaequ +x + y.
est autem BP: y:: dy: dx. fiet = Xdx = ydx  aequy dus
(2)
scribatur ejus loco =X dx - 2 y dy aequ _ fy x +  ydy
Si esset + X dx - 1 ydy aequ. 0. feret =L XX - yy aequ. 0. Ergo
Fxdx - = ydy aequ. + L XX - yy. Rursus ponatur fydx + Lydysa
(0
at
fiet: =+ dx + L du aequio fiet = X + L y aequ. 0 et rursus
ducendo per y fiet: +yX + + yy aequ’0 Ergo foret:
y dx + L y dy aequ. +yX + Lyy. Quod tamen falsum est
iddeo evitandae multiplicationes et divisiones, et res itamen
sam. = Xdx = L y dy + adyue aequ  y dx +Ly dy tady
jam x da Ergo Axdx- ydy + adus aequ+ ydx + Lydus +ady
e
jam S+ Xdx - = ydy + ady est aequ. = 1XX - yy + ay
ut vero invoniatur et Sps dxt ydu tadus, puntur fingatur
aequ. . fy dx + : y dy + a dy aequ. 0. fiet: = dx aequ. L dy + a dus aequo
C
Ergo X aequ. L9 + a ly. jam ex aequ. 5. est ifsydus aequ y dx adus
e
(10)
et Sydus aequ  L37. Ergo  yy aequ 4 Sydx-adus
a
(11)
jam si aequ. 7. multiplicando per e 2g. fier  yy aego 4 =xy- ayly
Ergo Afydx- adque aeqo = ZXy- 1ay ly. Ergo fiet denique
x (Fydx +  adu +: ydy aequ. =; xy t: ay ly + L yy
Jam f ydx tadus egeeet fy aequ.0
Ergo Hy ax + adus + Zydus aequ. 0 aequ =Lxy + L ay ly + L9y
ergo jungendo aequationes 3. 4. et 13. fier:
Y ZXX - yy + ay aequ = L xy + = ay ly + = yy
64)
seu: 5gy feXy +2ay ly aequ +2 Xx + 4 ay quae es summatix
(18
aequationis i. Et pendet ex logarithmis. Caculi veritatem ita
(16)
experiamur: 10y dy f 2xdy +ydx (4 2 a dy, t hal y dyogu taraxrdadus
sed hic video difficultatem nam si in aequ. 16. tollatur tu per aequ. 
habebitur dx. de per x. y: at idem habetur per aequ. 1. Ergo hos valores
jungendo haberetur aequatio absoluta. Quod an succedere possit
an
valde dubito. Et omnino dubito an procedat transitus ab aequatione
ad formulam..
Sita aequalio: