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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 1
# Folio 407r, page id 00068196:0809
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X 1 60750a
de quadraturis per summas ordinatarum
e abx d.
si p ommes possibiles edm combinationes
e2
a
nscuum ordinatatum inferiorum
curv arum procedatur, habebiuus omnes curvas superiores quarum quadratura ex dutorum
combinatione pendet: e. g. d + . A smea B  X. Ergo y + a b 
cyr 17Z
tujus ergo datur  dimensio: fiet aequatio: y2 + ab Za y2. inde: y q V + aeZ a ay
Ergo =y = aZ 1 a sab + a 2 et y 5 S 4 aZ + a sab + qu E runco copi
Datur ergo sumua harum rudicum, et si summa harum sab + q non detur
Sax + e ab BZ Ergo sax p Z =  hoc ax  otq u 2alyg + a b
et fiet 3 Z - y Z a - 2ab ) Z + a b 7 0.
sci
 quor
uit crdinat
Inquirendum est etiam in divisoris aequationum quae sunt duarum incognitarum  B
+ + X t F b C. summescilicet aut differentia X et b
X
Ergo  + + X + + bX p ac. sive
X1 F bX + + ac. Unde jam patet
pluriumve
hoc modo semper cum b est , affectuus signo +, alterum ac affectom signo
nisi uno casu quo utrumque affectiums signo F, ergo etiam X aequatur summae
aut differentiae ipsarum bX. ac. sic vetr (a a co)X (a co cd) b, C
Ergo (aa c0) X (a ) bX B Cd. sive X Y () (Cd a) bX (a aco) ca
 (a ac0) x (c04) b (eB X (BY CC unde fiet
varielates
(a a c0) X (aco a) bX B (BB 1) ax (B C) ca
3V) aX (C B) ca. Hac metrodo omnes formas signonum
aaco possibiles possumus indagare, et determinationes
etiam, pro qualibet anulogra necessarites
sed a4) b.
ita agnoscemus quoque ex ipsis formis aequationum in quas analogias sint resitabiles
Et in primis an agnosci possint ex ipsis pnalignis, an imaginari aefetura ae quationus
dr ciuce
neque enim puto unulogiam posse esse intelligibiter et tamen radic aginam
valores vel exattos vel propinguos; ut analogiae utur videntur habere ad loca investiganda
et ad mtri vilores Geometrice inveniendos, quod sape ope curvarum satis compositaram compen
esucend pun tunsi fiscs foles
dosisene fis, et neul aluo rester, quo into eas comnde