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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2b
# Folio 137v, page id 00068198:0274
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Differentia inter duas Hyperbolae ordinatas proximas
+ S a + X + 2βX +  = s a + X 1
Ergo Z  (2a + 2X + 2 PX +  - S a + x + 2 +  A a + X
. . . . . ..
1 +.
9u - a5 Y - 4 X + g a t 4 Ha X + 83X +x +D Cx + +geX n a+fa fexa +XX
.
Unde delelis alius fiet 3a + ba∞ + 3X H 0. Unde feret a Y) - X. Quod
den
est absurdum. Sed unde error
si fecissenus a +x ++ x + ( F1Z + V a +X
habuissemus +X + 2X + B F y + _+ X +  Z Sa +X
Unde 2X (Z Sa +XD sive AaXB a + X, vel a X  a Z  Z X 
vel
Z1
ax Hujus ergo datur quadratura.
Sed non possum satis mirgri rem priore methodo ventum fuisse ad impossibile. Nec video
curo fuit ergor calculi non praefixeram binat
vinomii quadrandi facto.
Sa +X
quaestio an idem sit locus differentiarum, ordinatarum ad eandem curvam. disfercutium
ex differentibus licet axibus v.g. an idem sit locus differentiam, inter ordinitas, Hyperbole
sane idem sempu  pro gressioni cuuae
et Asymptolon, et ad axem.
homogeneus, undecunque sumatur. Curvae autem locu sit ex quadratus locorum differe
Ergo et idem locus quadratorum ejus perptu locus quadratorm
en
em componitur ex loco quadratorum, differeatiarum, et loco rectanguto, rectamus uli autem additur
quadrata cutem loci qui.
aut subtructio non mutat locum. Ergo idem est semper locus dquadratorum, differentiarum
ipsius curvae. Ergo et idem semper locus ipsarum differentiarum, pois ex emiusta modo scilicet
Hinc sequitur ax esse
quantitates quae calculum ingrediuntur omnes sint verae
Restat tantum demontrandum, quod
ra
ordinatam Hyperbolae cubicae.
idem semper sit curvae locus. quod patet, quia locus est qui curvae, qui ipsi homogeneus qalo
a -rat 4 X sed a k = V a 2a +2 +Y
den g
s
1Z
4
in
opoemom
unom B. Curva
ipsa expleabit
duboliamn
B
licribola