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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 1
# Folio 185v, page id 00068194:0370
# Original at the GWLB: https://digitale-sammlungen.gwlb.de/resolve?id=00068194&page=370
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1t
nos remiratur, est e nova difficulias quod posita variatione isf
ipsarum t non jam ampli, dg haberi potest pro xt
videamus ergo an sic procedere liceat: X+t: g = dx. Sdxrau
= e. aequalio generalis. Sit jam data aequatio quadrataria
X = d X. de +d fet X+ +: 9 = X Assumatuu
en
aequatio nova t: g = X. 9 Harum duarum ope toleta
ope sublata X habelitur relatio inter 9 et t. Verum non
licet aequationem 4 plane assumere pro arbitrio itaque
possumus eam sic scribere: t: 9 = X: G unde habetur
quo nise cujus vula substitui potest in X aequ.Z ubi X est data
verb. gr. si esset X = a: raa -XX, fieret ex aeq. 3 feres:
X+ t,: g a: Siaa -xx. jam ex aeg. 4 est -  t g: g
et fet:  +g + +g = a9: Traa - +. g. g: 9 in qua sane aullus
est ervor, quia g iq dabet intelligi  potest a quemad
modum ret postulat Verum ex his videtur sequi si inveniri potest relatio
inter _ et g ex duabus aequationibus 3 et 4 posse etiam inveniri
ea atioveni inter X et y est enim C X+ 2Xt +F +g - y
de tollendo + et 9 ape aequationum 3 et 4 haberetur relatio
inter X et y. Et si quid praestaret arbitu, o relatio generalis
assurita liceret etiam hoc facere pro invenenda y non adhibilis
A et g. sit ix. sta d: a a Fraa-x el
fiat  = X sit du = dx Saa -x: a fiat y = X. et habeb
dy = d Z dx. et fiet saa - xx = d X quae aquatio debet esse
identica sit alia aequatio ady X = d  XX + yg ay fiad y
fiat y = X et dy - a X dx et firt adX X = XX +  aX quae
aequatio debet esse ideulica ubi notandum est X esse formula. quomodo.
cunque vel rationaliter, scilicet vel irrationaliter ex x formatam
N 5 - v +0 et d G adv 10: vsde si ergoi  sit X=
1. C
d
=
XL (8
sr  ax dr 10 (  +
P (+. Ergo a ( =  S10 av + v 48 O si ergo et
0 X =  ter axO (B 10 + ax O AB = xx + a5