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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 284v, page id 00067993:0570
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tam una functiones eanus, invey.
quad. circ. et Hyperb. ex se
invicem ex et alias figurus
figura proposita esto parabola, cujus vertex A. absussa
applicata CD - y = SaX. posito X, latere recto
EE infinitesima seu unitate constructionis = 1 vs
rentia inter duas applicatas proximas non nisi irta EE distinte
erit aX + a= Sax. quod si figura aliqua eogilatur
differentius applicalarum pearabolae homou enea, ejus appl citae
crunt: a axta - a ax. = y., vel utroque quad it:
axta + ax 2 a X + aX = 
seu 2aX+ a - Z = 2 a x ax, et ulioeque parte quadri ta
+a x + 44X - 4 X) + a - 2 + 7 = 4a X +  X
a
vel 4aX + 4 ak - +Xy a + a - 2ya + yt 4a 
siet: 4Xya = a+ y
vel 4X = a2+ y = a + y Ecce dt fi ordinitas
ad basium figurae
cujus ordinatae a axem sunt homogenea differtatis paratolae.
vel axya y a vel 4x
vel aX - a2+ yt
a
a
Applicatae Hypertolae sunt: a different ia a L a = a  + a - a x - a
X +
X+ 1
Datis difficulis a inverso modo quaeritur figuia cujusint differentiae
GW
Sin -
posito ergo GW = _, et, WdL =  erit W0L 
ergo
ED
p
erit  ergo
dudum
 erit: =
in
X
a 2 ED EM
 - p = a
EM
Jam alinde constat esse PE- ED = y d yrt yX +1 Posito scilice
WVL
y esse ordinatam figurae quaesitae nam BE
an
a
ED
Guo vel  = WL
alibi a me demonstratum ess. EM esse differentiam inter semiquadrata duarum
frgurae quaesitae ordinatarum, seu e inter semiquadcabum de vie semi
quadralum de y_ se inter V + a + 2)a et y =  + v
ergo
erit:
EM la
ad +G1)
es
sive a X 2ya = 2 a
Sive
sive rejecstis imutilibus: a y
Na
sive Y ab a- yX ae yb
XX + a
a
+, seu  Unde patet aequationem esse Identicanus
ac verissima quidem esse assumta, sed unde nihil
novi detegatur.
Applcata circuli: V2aX = X E, alia 2aX + 2a = X 4 - 1 + 2X, disfe-
rentia inter eas est: = y Engo = = 2aX - x + 2aX + 2 a - x - 1 + 2X -
D - 4a x + 4aX - 2ax - EaX = 4 a X = 2a v A E +  + X - 2, dictioque
seu  ac = Da et utraque parte in se brctu, tet
∞
2
Aax +ax + EX 1X- 4X, +. 46
e X gax
4+8aX + 4 - 44X -  ax + Bax, 4a - + aX - 4a + 8aX + X + 2X _A. X,
1Ca+ 164~ + 24 87 + 547 1 4X ax 1X 1 44 10 e 
Paeterca
ax + dX
ryx rarZ
cax, 2yaX
2e