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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 280r, page id 00067993:0561
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Gothose si frinctum Lesgiti
Luadratura Arithmetica
De vera proportione
CIRCULI Ad CuAdearum dumo
in numeris rationalibus
simplicissima serie expressa
et demonstrata
praemissa est Exercitatio
de Maximiset Minimis
Mich. Angeli Riccii nuper
S.A. E Cardinalis Eminentissimi
et alia quaedam ab aliis
Geometris praedemonstrata
quilus trus quorum in prasenti
demonstratione adhibita
Ex Ricci de maximis et Minimis seu
proprietate tangentium demonstrabo
quadrations pouraboloeidum et Hyperbolae
duco; hinc demonsteibo quadraturam nc
Arithmeticam  praemittan
et Hugeni quadraturam Cissocidis
excerptam ex libro Wallisi de motu.
quia et exila demonstrare possun
A dimensionem pldeature
nea meae curvae Rrationalis cir
culo sga condimensae. Demon
Arabo et Ciculum esse incommen
snabilem quadrato diametio, quia
enim nullum ciro polygonum inseri
iptum vel circutus criplum per su
ex
ua
ationem quadrantis focctum circulo
ommensmabile esti lina nec erit circulus
aba qe ee ce aim
consequentia tamen rigco rose loquea
s non satis manifesta differentia
inter polyshonum aiqud intripotum a
circum scriptum, mbernm 
ferentum minor quam lindi mensura
8 1. operae pretiamest hoc regorosum
edi Addatur figura aepe express
melior ea quae idita est in actes
sipsiensibu. Aldatur e simutie
quadratuatyus perbolae.
ad circumferentiam super  in
duantur MN, et CP.occurrentes ipsi
ipsi AB. eut CDH 2MN. et MN nG
et CPr 2 MGC AB
AB
B
jam Triangula ACP, et
a- M9
a
quae est aequatio identica. Unde ea hac modo seepe nos fallum
BL
LM
a H An H
 1G, et paratelae
em
Jam
1C1
Porro ob Vla similia ABL, et C PA.
aMN  2 AB2nG ob Ita AV ADC
ce simulra, quia ACp2AM.
praetera Triangula Et B, AMB, CMG. simlia 4G aequalia unde  CZs, AB.
et C P
a = 2a 42 MG e 2MG - a
seu P2r
ap, AG.
GAB. ut idem PZ
12 AB  MG fiet 1G
ha
(BM a- MG  la BML, et GMa similia.
a- BNN iG
porro AN, BM  NB. Ergo PG ⊓ a = 2 BM, et BM,, a- MG.
ergo PGp
poro
at
a
Pn 2nGCD HCn
a.
Ego M ob Vla ABG AGB, NGM si mili a.
unde MN ABMG
Lep AL
ACH
4B
inde  n MG, + a L M (= L M MG
quod non aeque faciunt literales,
rgo mutendum aliquid
ilem na Mo
GB,
ergo MN,, nG
L B sunt similia
ergo Atn Amtem atMatn  cin pe
AL
Ac p G em end
A B
1)
A B
AB
aA62G
et explicando PG fiet rursus ientica aequatio
C p- CLpC1 18.
A1
e b