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# Title: Leibniz-Handschriften zur Mathematik LH 35, 15, 5
# Folio 47r, page id 00068207:0093
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Ad Antonium Arnalium
   E
se
Theorema invenigenerale (cujus demonstrationem c
transse cum sit prolixior hac tansferre commode
qvo
hic supponere suffecerit) segmentum figurae
aequatur dimidiae figurae  resectarum
verbi gratia segmentum ACA aequatut dimiduae
bigurae AB AE ABEA, quam voco figuram
resectarum, quia curvae Ipsius curvae AE, ordi–
natae BE, aequantur ipsis AT, refectis
am  per c4 tangentes curvae pripcipatis AC
AC sit arcus circub
net
radie
et centrum G vocando AB, X et BE, y. calculo reperietur
yy
seu
vel TE
tune E
C et radium 2. calculo reperietur LX aequ
14yy
aeqal.
yy- y +y -y etc. in infinitum. (Nam
maltiplicando hanc seriem e infinitam yy  etc. per 14yy. rod
Est autem _
gis
prodibit y Poetosumma omnium yy-y +y6- y.  ommium
yis
seu omnium LX sive omnium , dimidiarum  E, hoc
seu Omnium gu
3
= Y + y - y
Lu
est  dimidia area figurae ATE A) est
(ex notaqvadratura parabolocidum, nam summa omnium yy est 
5, et ita porro) jam dimie
u
al
3
9
et omnimu y est 
subtracta a dimidio rectangulo TB, (EXy seu Y, seu y - y + y - y ex
+yy1
demonstas relinquit 2 y- = y + b y -8 y 8c. pro dimidia area figurae AB
divror
e
p
AB ss seu pro valore segmenti Circularis ACA t centrum circuli C. addatur
redur se
q
ab AGC segmento ACA, triangulum AGC (seu = BC in (BAG. Est autem AG, X et
nam si
unde ZBC est Z seu y - y + y - y + y etc)  prodibit pro sectore AGC
rectat
anferem
e
14yy
= y + y etc. qui est valor semarcus. cuiquecum
tanglus Kauterica seu Triguaometrica sit u
Si jam arcus ANN, sit quadcans circuli, seu C incidat in N et Tin M
A2E valor y - y 4
e
a
tunc E incidetum N, arita y aequ. 1. ergo quadrans circuli erit
lector quadrantalis circuli erit 1-  +  =  +  si radius sit 1.
vel circulus integer erit ad quadratum circumscuptum, ut +- +=-= +  et
est ad unitatem. q
8, vol. 1
sequitur  radio existente 1. et tangente
artus existente . ipsum arcum
fore 7 ..
4 y - y ek.
5
pa
e