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# Title: Leibniz-Handschriften zur Mathematik LH 35, 1, 11
# Folio 20v, page id 00067970:0040
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V (14)
fiet b aequ n +n  22 mn
(15)
(16)
Ex aequ. H. habemus m -n aqu. f aqu. - b f 2b sm. d
ex aequ. 14 habemus m + n aequ.  aequ. be + 2= mn
fiet: m aequ +Y et n’aequ  te- 5
sive  per (. 16. 18. 19. fiet
(21)
m aequ. F4F un f4b n. d
et, per 1616. 18. 20. fiet
n aequ ob += mn b m- d
Quos duos valores substituendo in aequ. 14.
fiet: b
Et multiplicando inter se
aequationes 21. 22. fiet
(23)
nn aequ = Min -bn + b d + b mn f6 smn
sive per aequ. 11
 et ordinando fiet:
n qu aqe bno
G ne fVx ma (: bn abdr B aqu. d
Aset
rigere + berma - = b n - = big 4b d + 2 b aequi0
e
sive
=Lb mEr
e per 14
b f. F mn
un (f bimo) (1 69) (4 1r mu + bad (rt b) aquo
unde per felicissimas destructiones fit:
me aequ. bd Sg-r
dal
ad AG ex data
(28)
obtinere potuissemus, quirem
m + bdr sq. r aequ. f6  m. d
sive
(29)
m + bdr Sqrm cequ. b m - b d
unde putet
Unde patet pruoblema esse platia
fietque:
mI Abarra m c
Ergo fset:
 2bd
sine artificio sex calculo deducta, quemadmo
2b erquq. rt bq osibede Fibdsq, b9 1 d
Hon o tberst
L vorsq. r. P. bq aequ Sa vuer b22 A bidra sae r t b 9
et compendii causa ponendo q aequi sd Unde lut constructionem breve in nauciscam
id ensm in nostro arbitrio est, fiet ex cum possimus q sumere pro artetrio
M aequ b8 - g uber 60. n + b1- quel r assumere pro arbitrio
faciemus in ideo in aequo 29. faciemus. bdnequ scribeent
  cd seero M at  aquh- bd
4 ficta
et faciendo taego f. dergr bt aequ. 2 d
Cbil dego 4 i taro sidceix adds. e bese
enim ingredi rvel qui valorem sipsius in
+2bdsq B aequ
= i mn
tn
(5) summa +b Z erbdsaer a nnn + 2mn
lesqu
b aequ n n
+ b aequnter qu m p
 sp 4.
u
Hcst
et qua
ster fiat sbd qqu. 9 seu inter po b et d
quaeretur media proportionalis
itemque recta +2D-29 d aequ. +. quaeratur
media proportionalis inter 4et s. ∞
itemque
E Hijus Iorm qu si alterutria quadralum
posten dificile ipsius in quadrato addatur aut ab
quod
eo adimatur habebitur man, vel
valbia aut
psius m
quaesitaque constructio est
Quae constorectio est tolerabilis nec
calculus ipse longe altius, aisurrexisset
Ergo m +noliqu. b
et m-n aequ.
Unde patet problemue esse plaumm am ipsa  problemata Elementaria, quale est
aequationes inventa sunt; id est ita, ut qui ea
ftdsisu habeat usus, plune ad ermenda plerumque
sed non et quidem in numeris facile resoluetur
sed in sed t constructio eju
reddam
i constructio linearis quae inde ducetur
corea
in prssimu
satis prolixateritqua
ni
q. vel, pro arbitrio assumere
quam ut nemminia
tem confraham
intram
dataequantitati aequalem
 f
ita nqua b
2 bd aequ  ber squir- b2
instituemque
eu  d aequ (14)
+ b aequ. ntn =
 Sg  aegu.
per aequ.
k(26
Abd qrer
M n. ad quadratum cujus latus. n+n
et mn. habebuntur ergo m et n