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# Title: Leibniz-Handschriften zur Mathematik LH 35, 5, 4
# Folio 25r, page id 00068022:0049
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Ulnum optaram ut et VD fieiet VWV. sed hoc calculus regat, experiar
demo. a Quadrato DL a + aax + anferatur anferatur quadratu
VL ⊓ _ ex seu a  a ax +X, restabit SaX, seu 2aX,
Ergo DVY Tax,
SVW. quod est verissimum Est
ergo AD vel AW ipsa parabota generatiim. Huc usque ergo
plane sitiffactum est voto. Sed jam in cipio vereri, ne error
sit in illa suppositonee, quod scilicet DE AV, DF Yd, et PX
BQ p Y+ (B7
Inspere tiguram hic ascriptam, in ea.
22 p BP. a DP, DB
DR, DQ. B X.
a
2DT,, QF 1a0
FBH FN. Ergo BTB TN. et recta
BF_, angueum BFN bissecat.
jam FN , X + d. B FB.
et BR F DR in X + DB seu a.. ergo
F B H FN  BR Y 8X+ a
porro
2)
QFHI _ 2aX, addatur 2  a, fiet:
a + 2aX, ejusque dimidium Et quia _qD dimidia
ipsius Q R. erit  es ssu DF ipsiu QF. erit TF
imidia ipsius RF, et BT ipsius 2 F. ergo B7 sarax
quae in figia prima primae paginae AV.
+
q
ab ejus quadt
auferatur a quadrato ipsius BF
quod
X X 4 eax 4X + 4ax + a restabit.
_ IX + 2aX
+
N 2X + ax  TF2. ut supra.
a BF atur Item a BF~, seu 4X +4aX + a auferatur
2F2
N 8aX, fier: 4X + 4a X - 8aX + a2
e et erit
B89 B9
H+2X + a sive erit,
DQ. differentia inter X et a., qua2 et dudum constat
stenim utique BE. differentia inter D9 et DB. Unde satis apparet
non esse BT equale ipsi BQ. nec ideo in figura pumae
paginae prima AV,
est parabolica generatiili
D9.
quare nec AD curva
evenit. Sa
eade; ut in cycloende
abx + a inferalio FF Nunc BT appellando y,
fier:
X Y
fier:
et erit
a erax
y et X  4y qu
16y4 - 8 a  + at, inseratur valori ipsius YFV
a
+ a2
16y4 - 5 aey (a)
ear
A ay
N2
+ 4γ (a)  , 16y- 445)
2a2
ut supra
+y sive p 2 Sa unde aequatior
2a a 1-
uus tatus quae indicut curvam ADE in
Fo. t feginapam Euus pturte esse pumtolimo