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# Title: Leibniz-Handschriften zur Mathematik LH 35, 11, 9
# Folio 1v, page id 00068182:0002
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lecare rectam in extrema et media ratione
Analysis indeque deductae tam constructio Linearis
sit recta ule canda
quam appropinquatio numerica
A quaeritur punctum sectionis B, ita ut sit
m
AC ad majorem BC, ut BC ad minus AB
BC erit a - b et fint ab = aa + bb -2ab
seu bb - 3 ab + 3 aa = 2 aa - aa = 5 aa, seu b - 3 a =  s5 eritque
AC sit a
AB sit b
b = 2a - 4 15 seu b = (1+ 2) a - a H1 + 4) Hinc constructio
erit talis AB Rectada data AC addantur tres dimidiae cd, ab eadem
detrahatur quarta pars AE ad datul dimidia CD, et rursus tota DE asqualis AC
et ab eadem AC detrahatur quarta pars AF, Tum  super FE descri.
BA. AC = CBqu
bame seuncirculus
FGE cui ex D educta perpendicularis occurrat in G
ex jam ex D ad partes A sumatur DB aequa
lis ipsi DG, eritque erectem B
B punctum quaesitum demonstratur  ita:
Nam si AC sit a erit AD ex constructione
AD.  (1+ 2) a, a qua si detrahas AF a
restat Fd (1+ ) a currus dE est a
ergo DG med. prop. inter Fd et dE, erit
a ((1+ 2), cui si aequalis sumatur dB
tunc erit AB, _ seu AD - DB, erit (+ 2) a - a (+ 4)
jam quia AB seu b est (1+ ) a = a (1+ 4)
=a + a ( = 4 comprobationes duas
1
utique fiet
Hini comprobationes  AB = a + = a - a V1+ 4
Cen
Ninc
prima
 BC = -  a + a. 11+ Z
Ergo AB + BC = a X
segunda AB in B AC =
aa (1+ =) = aa (1+
secun B C quadrat = 4 aa + 1+ ) ac s- aa Y(1+
da
seu
aa (it L)= aa Y (1
Ergo AB in AC = BC quadrat
15 = 24
236062 + etc
1000000
Ergo AB = L a = 118033; + et
a-
1000000
481966 + et
1000000
seu AB ad AC ut 481966 + ek ad 1000000
2
500000
118034
481906
Figura paginae
versae Huc transferatur
tre
e
14) = 2 1