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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 128r, page id 00068194:0255
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dseptembi.
1680C
Novum mirificumus inventam pro rangentibus
Inversis.
sit quaecunque aequatio ad langentes invesas 
3
in qua y. yy. P. dy dy dy. daque, day et.
X.
2
XX X ex du du ddx. ddx et
pro y. sumendo a. vel b vel c. crc. pro du b- a vel c - b.
-
dus
(dy)
pro adus fiet lyee (tys)- dus seu c- b, = b-a ic a
His jam positis habetur aequal et loco dy. adque, et itqu adque
porro substitutis, habebitur aequatio in qua praeter terminos seriei
supererunt X et ejus differentiae qualescunque. sed ut datur aequa
tio ex a. b. c. per x. ita datur ex 4. b. c. d per A
etc
per X 4 dx. His colcatis tolli potent x omnesque ejus po-
tentrae, vel olis tantum ejus differentiis, quae cum possint
pomi constantes, evanescent differentiae differentiarum
Hinc sola supererit  restitutis jamb y. dy. dyy days habebilu
aequatio in qua sola supererunt ista. Cum dx vel adue. ipsa
lisera X. sublata  aut etiam si cillere A notimus, poterimus, sallem
sin tollere ut non amplius ducatur in dy. vel in y. aut simile.
Hoc facto habebimus X ductum in suas tantum differentias, et
X y etiam in suas tantum. Ergo res reducta ad solas
quadraturas. Quid si sit Y ACF F Cadudus X dx
aequa sio dad rectam
video nos adhuc haerere nihilus hac diligentia actu im esse, 
imo nonne licebit facere dx B constant + ergoddx pio.
et dd ax p dx si dx accurate considerandum an hoc liceat
si licet, res confecta est: dubitare licet an tale 0. defmal
Certe mpr destruet, si in numeris finitis ipsi infinito uppro
praquantibus utcunque res sumatur. Rem puto vere sueceden
Mica estire transitus a seriebus replicatas ad calculum
differentialem. Altira alteri auxiliam ferre potest
contrahendus calculus, nam pro transitu et retransitus
potius ad hibeamus certum manendi modum.
Res succedit nam si in serienfint probare vel per eass
quaesitum yt invenire velis utique d dax evanescit
e