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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 3 (shelfmark LH 13, 3)
# Folio 77r, page id 00068200:0155
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Habemus ergo aequationes
et
2ed
OII etd
9 II a= g2
16n
et
g
a
e sa-e
161
e
Unde patet,  eod (ut obiter dicam) g eodem modo
scilicetre
componi ex e et d. (medium est harmonicum Y( ut e. inter b et d est
medium avithmeticum geometricum Quemadmodum supra jam notavi)
Ex aequationibus 1. 2. faciemus novam, in qua absit litera n.
ex aequ. 1. valor ipsius  16n, e inveniatur, fecciemus:
(4
16
ut
(7) gd
16n a- gd7 16n ag ergo n
c
seu ratio numeri 161 ad
a d - a9
est composita ex duplicata g ad a, et simplici d ad d-g. seu ratio
numeri an ad 1. est composita ex ratione g ad a et supduplicata
d ad d-g. Eundem valorem ipsius 16n rursus quaeramus ex
aequ. 2.
C
92
(6
a-
 ergo 16r5, eaudem quam ante habebit
V
16n
valoris formam, tantum pro d ponatur g, pro gponatur et pro
1
g ponatur e, fier 16n
aequationibus 5 et 7. fier: e
seu
e +
f
e
gre
v seu d
ergr: aequando duos valores ex
2
d seu
d- 9
e
2
-1+ 1 - d
v
seu d
92e gr
2
20-G
supra aequ. 3.  eg +dg⊓ 2cd. seu dp eg
ergo
e
209
2C - 9
2
A
Ergo
M 20-9 seu 2C - egp 202-9 Unde
manifeste patet alicubi commissum calculi errorem, alioqui
haud dubie prodiisset idem, tantum alicubi pro e, positum g. sed
hoc facile enendatur illud vero notab Notabilis autem exitus, qui hoc
e
apparet si scilicet in aequ. 8. ex 5 et 7. faciendu, non ebannisset a
habuissemus universalem irculi ejusque partium quadraturam. Hini tam patet
eam non poss haberi. Nam si haberetur analytice haberetur arcus sectoris,
utique formula ejus esset eodem modo composita ex C.. quibuscunque a
ide
and subie haberetur id est si quaereritur ejus valv ex datis e, ghaberetur
formuala tals eotem, modo compesita. Et esset otanti padam gitione