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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 22
# Folio 4r, page id 00068235:0007
# Scan: One image of two folio pages side by side, registered by the library under both labels (also fol. 6v); this page is its right half.
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Q aqul lam
bb aequ la b + maa.
equatio unan
eri pocest. Sesu
b incognita. aequatie unam solum habet
habetradicem veranum subtrahatur ab ea, ipsa a
neru subtractionis seu quotiens, divisionis sit 2.residuumC sive
un
sit baegu  2a + c. fiet: 22aa + (2) 2ac + cC aequ laa
et lac + maa et ordinando:
CC aequ. + l ac + l2aa vel + l2aa X) 2H aequ (2) ac + cc
-1)ac + maa
2aa
 Lac
+maa M
- 22aa
uet jam aequatio nova cujus incognita est C, habeat etiam unicam solum radicem veram
utrovis modo debet l2aa + maa - 22 aa esse major nihilo
seu l2 + m major quam 22. et m major quam 22 - l2
et n major quam 2 - l. scribatur l2 + m aequ 22 +n.
fiet: 22 aequ l2 + m
n
si n aequ. 0 foret 2 aqu
nunc 2 minus quam
22∞l2 + l aequ l + m - n. seu f2 4  aequ Sl +m - n
4
ergo 2 aequ. +  + Se +m -n est autem 2
(2)
t
minor
quantitas affirmativa, ergo vel + aequ. + vel l mujor qu
posteriore posito meresse priore casu 2 est major quam L. posteriori
oine Hinc ta ex si + est + erit 2 p 
si mun pi L  Ce et = est + erit 2 p l.
Si m - n Y 1 et = est + erit 271.
si npi m  et = est 4 erit 27l.
Si n p in erit l pnqm. quocunque casu,
Ergamsi l e  cinit
Ergo si
l B =n + m. erit n e m
quo sedus sricmit
nondum dicere possum cu comparetur aequatio cum ista:
compar c + 7
+ Cc + eβ = aβpo.
cX
 major
Hine si radix affirmativajor.
negalivae f CC ∞
fine si radix affirmativa X, major negativa β. fiet
CC aequ +a C + ∞β.
Sin contra fiet:  CC - aC aequ a β.
Data ergo aequatione bb aequ. lab + maa erit radix affirmativa
major quam negativa. Ae jam si n a a radice b. detrahatur
2 a. ipsa quidem radix affirmativa decrescit, residuumque est C.
(quod est minus quam a) negativa vero crescit, quasi esset b+ 2a.
unde cum negativa sit major quam 2a erit et major quam a.
ergo et major quam C.
ec +(y aC laequ. + l2aa
+m a
aequatio itaque sic ordinanda est posteriore modo:
Hire pater esse CCaj 2 p l. se 1 p 2). 1 sipua lara p 1