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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 91v, page id 00068201:0182
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Universaliter loquendo, ac ne ulla fiat suppositio satius
est facere p pagb + m. p Xt. Ita enim
solutionem tam mirandam constantiae imprimis debeo
nisi
non permittendi ut aliqua ex incognitis ad extremum u subi
calculum amplius turbare non potest; descendat in denominatorem
orro Aequatione altiorum dimensionum frequen-
H-97 e rresr
4 ef n 1d-q. ergo
f⊓ 1d- q
4e
+l
l
quaesiti vel d. X. DS
tissime ad quadraticas revocantur, seu X. 9. semper in in tegris habebuntur
Solutio etiam semper in interris fiet, si modo
numerus
ld-q diiide ta numeri dati sint integri,  recta +, tali assumto, ut
pone 1dr Cgl + hH.
fier g1 +h- q e sit multiplus ipsius ba.
Quod si ea. b. ponantur fracti
uon ideo minus res succedet reductis enim ad communem denomina
et h emgltorem fractionibus, poni potest , ejus denominatoris multiplus.
at gl  1d- s Obiter hoc loco exposin Methodum semper destruendi terminos
2m
fer h cmldeli cognitos ope duae duarum aequationm, semper ergo obtineri
Id
nullus
Hoc nilus 2m. potest aequatio, in qua non nisi unus sit cognitus terminus. Idem
est un
1d sit vel quadratus
vel jam summa ducram
tamen facilius fieri potest. Suita duae equationes arte generali, qua
poterumt pro arbitariis effici potest ut quaelibet aequationes proposita unum habeart
quadialorum, quae sumi
e + m
ld- 1 C2
terminum aliquem cauciscatu eundem cum quadam data.
ldqusi quis exprimere velit Analylice quantitatem positivam exprimat
quadratum, aut compositum exquadratis, aut ejus multiplum per numerum
Ergo 10(qea
datum Cognitum pro quadralis exsi aohiberi potest alia potestas, cujus exponers par.
Ergo A (71dff2 Unde et negatiou. anal lice exprimetur, negaido) attirmativum
ai quis exprimere velit Analytice fractum, potest ita facere
et  frai
1d- qu flerqe 4 bl + dL
tent ed294
aequanus quodratosit formula
a lest fier
summa enim ex his duobus est infallibiliter fractus
Mia signatur
cV - qur
db
Sive cl - g, cqusa
2c
qc
integros, sed prrod
q Lgnatura univerhalior
fieri potest ut dividi queat per b.
 qotas si b talis assumatur: 1Xc l. , flg + Cg2
NF1
2es
+c2
- q1u
si imo error: dividi non potest
dl+ 39  sd hoc hbed usum contractim, ut si drta sit formml
2C1
esis modi intellius
Vatar qua libet quanti tate Qvadrato aequanda efficere Aequitio-
nem ex qua Radix quadratica exacte extrahi possit. Esto L4
Fac 2de r l9. fiet C
Estotalq P C + 2d +
c- d p 9l Esto 19 ⊓ 4cd. fiet dp a4. Erit erge. Nt4)C + 19 c. et
Erdd d nal fiet.
Ergo 91- c
Ergo sic quidem
la p c + 1l9 7c
et Radix. 
2qu + q
c
+ lq
et
1
v fiet oppC - l40+
7 0
Esto jan A
qu
6c
Hinc semper quaeratum resariri
um melludo pero posita, cognita incognitave maneat quadratum: sivi duo quarata
intervallum quadrato quadratus, vel cabus; vel summa ex illis. sed ha etaru eantibus 
possit, quod addita subtractam quandate ((2b)
intervalli dai analytice propositi g. in qua duo quadrata invenire quoram
fieri potest
solvi pt quau
ili fractus