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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 243v, page id 00068200:0488
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ce differentiae ergo:
=TI. = X. Herum ergo
+a = X
t
a
a
siumma circulo sgntomos.
Jam: 2 + 2 + L + L et
et 1 + 2 + 3 + 4 etC,
summae semper X. Habemus
ergo curvam parabolicam simubus
circuli sgutomem ab eadetm
etiam Hyperbolae syntornos
hinc rusus nova videtur method
oriri circa circuli et Hyperbolae
Comparadem
Ergo sutuma est
resa
AX F X jam 4
la
vel2aX - X= 2ya, fiet 2ax X- a
Xa = Srya a, seu Z= ina
vertes
posse varias figuras syntomos,
ut modo haraloolicam curvas
modo Hyperbolidam Hyperbotae
se syntomon gro Circulo
C
2AX - X -  =LL
e
ut habeamus curvam cujus Elementa
crescant ut sinus circuli frimum
ipea curvae Elementu descent
sic:
2ax -+
qu
e
ad
quadrato 2aX- X subtrahatur quaa
a fiet  residui radir:
tum unitatis:
2aX - X
2
a
est series differentiarum
V
figurae quae circulosentomu
.aa
inveniendi
fo
I
Sax+X (-
a
ax +X-
a
2
hnc habetur modu
pro curvam quae eadem cum Hypertota
= X
a
+
a
fiet Xax+x
2
2
Jem sygmae tujus
pax +X a, summa simin potest, ergo summarum istarum series dabt figura
abtraratur ab ea H
cuius curva Hyperbo laegutomos. fatumodi
ata; ax nge
posto 
atra suo
O
vaetati curvam Circu circuli simubus sinta
fiat autem aX+ X = a = V. Ergo y = a
c
vel 2a a + a +y = ax tx +ae. Ergolia Fy = a+X
s
 qc
hoc modo sibi syntomo
sa + y = X. Ecce ipsam Hyperbole
it unc prole nolandis hic per ex ignas muta trmenlas fierro
quadretur, fiet
reserquatur  fret