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# Title: Leibniz-Handschriften zur Mathematik LH 35, 12, 2
# Folio 159v, page id 00068195:0318
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a
X+b =
X + xb
unde fiet, LaX- 2a. Ac proinde intelligi potest non
x
ratis differenlibus.
dari in his regressum, ac posse quodem statim diffeentias at non series differenturm, datius diffe
rentiis inveniri quid amen si faciamus: a + a2 ha ab posruta
fiC xres eodem redit. Et ratio
est, quonim cum summae tantum, non differentiae indagentur, nihil tollitur, atque ideo dendque
abjectis is quae ipsernemo b affecta sunt, res redit ad priora.
ax- axta. homogenen huic a. Hinc intelligi t Quantitatem curvae haberi
posse, quae hyperbolocidibus cubias homogeneu est, et ita haberi summas ejusmodi etiam subtractiam
Nota ut quadent
X+(
fogra inearum non tantum quadralorum haberi posse
supersolida fignis ita et lineae curvae figuris homogeneae sunt. Et in eo consistit
feurati methodus quadrandi curvas, quibus sunt homogeneae lineae quadrabiles
Ergo a - X = B f 2βX. = a + X +  restat 2X.
a - X= 7. Ergo Jam X X + B Culice X + 3+ 2X(+ (3, fiet ergo 3X.
Ergo y = a - X fiet ergo jam X + (3. culice dat ∞ + 3X (B+ 3XB + β, fiet ergo
Eue ratus quaraunam Hperbolae paratotae et posito pros y 2) a - X, fet:
y, fo sive
37
= y sive y’a  Xy = 3X
Ra Y, = sa - X - β + . (3X = x () Ergo a  x 4 a 4  B
ssa
per
P = Na XC (A2 x +a - X Z 2(X =
a
a = X
3
1β) a- x
Hyperbolu ABC. Asymploti DE, D DF. Et X = a et y - a
spatium quinquilineum BE DFAB. Habet momentum omnium Y ex DF
sunt enim a homogonea applicatis, ilem omnium X ex DE, sunt enim a quorum
series homogenea seriei applicatarum ad Asmptoton Hyperbo loeidis cubicae, a vel
Ha Omnest X. Rectantulum XY est Y ay = a.  si vel ax a.
24
positnen Y Ds. etiam DE = C. X
Unde sequitur Hyperbolaideus Cubicae quadcatura. Duplm
on
in Xy
quadratis omniuum X ad hasui ad DE. et omnium Y ad DF applicatis aequatur
Ergo si ABC sit cum Hiperboloeidis ubicae, suma area spatii quinquilinei
foret Quod ita ostendo:
moti infedea