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# Title: Leibniz-Handschriften zur Mathematik LH 35, 2, 1
# Folio 100r, page id 00067993:0199
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+ete est . ot
Bon BC
Ropoptio
autem muneri, 8. 24. 48. 8. quairati a parium Si set f ct unitale miguti; et
numgeri 3.8. 15. 24. 35. 48.63. 80 et quadrati dagupurium quam impiirium eadem unitate minuti.
pro
Natu = +  +1. +  etc. est 2. Ergo dividendo omnia ser 8,
+ = += f += etc est. quae prier est propositionis hujus pars.
2 48. 80 12
ad aequil. 3
has duas sent
Ergo acitendo utrum haum
Qua est propositionit hujus pars altera.
manigem
orn
mingiet. 38 5
Echotium.
His ita positis puleirat quasdum consonantias libet contemplari
+
oposit
18 83
B itque 4 +L 2at etc est 2 per pros
11L+I
 etc
140
cujus Quridratur
Hyperbolaes
inscriptum
 pars propositionis ) et 3. patet ex prop praecedenti. Prop. parct 2. ex propleca pars 4 ex coroll. 2. prop. sux erst
Sie ut consensus circuli et Hyperbolae non inclegani clarius appareat, figuram inspociamus
sit Hyperbola centro A. vertice aequilatera cujus centrum A. vertex C. potentia 
seu quadratum inscriptum ABCD. crca idem quadratum inscriptum descriptus sit circulus.
pes conelli prop circulus 2D Attoc quadractum sit. erit circulus, fa 5
pe coroll. 2. prop.... et spatium Hyplibelicum Circulo quodam modo
c
196
ex ultimam 1
etc ppinis circuli
10 et F-
respondens, CBEHC erit  et ete. Qu facile ostendi
potest. Nam si esset quadratum isset ABCD esset Y.
stiam lats eus AB. foret 1. sit  Y Ex natura Myper Gatic
u
Hypibolae
 AMet AA B.  AML rectanus. aequale quadratoC
AB(D ad eoque AH in ML est AB et ML est . seu en
AIL est
AI
AB+ BM
AM
sive ML est AB-, BM  s +  B )C  Rse
1aA
(per seriem prg regulam inveniendi summas progressionum Geometriam
desrescentium, supre prop. .. quia BH. est minor unitate AB adeoque
fractio, cujus potestates decrescunt) Sma autem omnimm
HL est: sumuri omnimm LB AB fit es tntangulum
AB applicatorum ad BE,, id est essius rectanus. AB in BE de
la
summa omnium BM, seu demto sent dorato Ultimae, BE, adeita
vsa summa omnium BM, seuBE demta scuma omnium Lt BM
3
iA_
seu demto t BE. etc. id est quin BE. est aeq. AB.
l AB.
fiet
seuma omnium L seu spatium C- a BC,  usque ad E H, seu
 eC
Area tpatii CBEHC, aequalis AB -  AB + L AB - 1 AB + 1 AB - E1 1B
es aa
sive
sac
sive, quia posmimus Ab esse L ideo
et srea spati C Bede
ea