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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 60r, page id 00068197:0119
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Na
ve ab v = C v0 + ab -a00 + 4b7
Detsa primi inter se
s
y S15
vv+ ac = aa0O+ ac D7
3D NS
aa 0 + ab DD in aadO + ac D) sit quadratus. 66582 quae
Hinc si suit  et D simplices
aequatio si identica, (vel ent O0+ ab = e66 et O0+ ac =  4G
Erg Hoc fieri non potest si vel erit
e
Od + ab e5C) et 00 + ac = a 59
s
quod non licet. Sed nec licet ()C + ab = e 6, quia dua
radices ipsias dO + ab non possunt inter se haber rationem constantem
Ergo sit O =  2 5 p = 7) fint AH22 + ab 82, t
+
Gt44 + ab ZFDD, in ht427 + ac 7
XB
A4 
2
8
te
8 m8F
 ort 696 vel 58958
Q Non por si 8 18. non potestesse 
quia non potest esse quadratus cum habent redices H t + _G -ab, tiqu- 2DS. ab
quae non possunt inter se habere rationem constantem
fr
est p+
Ergo si sit 8 si sit 54B poterit esse 8&  in 5056
sed ita tt 22 + ab F CD)  et tt24 + ac &4DD, habebunt
radices communes blnas aequales 56  sed hae radices
sunt nempe hF2 2 + + DY- ab  Z2 - fDY- ab ab una parte
2 + 7 -ac in 47 - 8BV- ac
alius qui
ab alteripate
 AB continent SS et CD etiam continent 25. tunc vel ex hyp.
sei A non continet _B, neceBCL ponamus  continere 85, et C
si A vel B continet 66 ergo t4 + ED.- ab = eb0. et
tZ(+) ZDY-ab = 566 Ergo t4 = C85 + 4) s- ab = f 88+) Y- ab
bH.
seu (1 -5) 56 = _  Y- ab (:() s -ac, ZD, quod non licet
 si sin sit N si A non continet 88
non e s, ne est res non procedit alioqui
et A
Aforet BQ et et B foet F
isi ergo A et B haberent rationem constantem quod non liget
Ergo opti oportet facere AB nec liceret facere AB ,88 46, et Cd a d et
neque enim possunt inter habere rationem, constantem
suprest at sit ABCd = 66 O sit A0 A non potest esse
quid si sit SE superest ut sit ABCd = S+ si nulla ex ipsis
A vel B, vel C veld sit quadratus, forent binaeaequates ex ipsis aequa les
quod not licet, si unus sit quadratus, velut A = 3D restabit BCd = 927c
si nullus ex his quadratus eut muisus aliquis ex ipsis e vad alteri aequalis,
isin generaliter provo probo vel omnes A, B, C, d esse quadratos esse
debere
1 L 8
A,B, C, d = quadial.
potest generaliter dicis. ABCd = quadrato, fore quadratum 5899DBDD
nam si S_ = E, redit ad 64dO. Ergo vel aliquis ex his AiB, C, d,
est quadratus vel bini ex his aequantur inter se, non posterius ergo aliquis
2
est quadratus vel a A = SY. sed pari argumento cum supersunt BCd = 458
sequitur vel rursus aliquem ex his esse quadratum vel bino, aequari, ergo nusus
B=4, restat Cd = 6, ubi par ratio Ergo si nullis ex his A, B, C, d, est
alteri aequalis, quilibet est quadratus sit A_ = 66 et B=94. Ergo
A-B = 8 =  set2A- B = 14D E Et fiet  YD = A1B
uro 24d= 84 2, B  4
7
SFN