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# Title: Leibniz-Handschriften zur Mathematik LH 35, 13, 2a
# Folio 137v, page id 00068197:0274
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SiQuarritur ( san bgus
C+ f yy
et earum ope porro ad ratioales.
dy
reducenda ad quadraturas conteas
sit y  1osxim, xen + 1 Sxtm, rp + 1 TXEnKIP.
as
12. 12
G 21.1. B D, 1. 12 nb
Eodem mods  fiat x et vV pro 10, 1, 12 porendo 20, 21, 22
5) Z et 23
30731,32
Debet esse a + B a L bgy = vV et 1C+ fyy 2Z
fiet a + 10. 10 mubt 11. 11 mpb f 12. 12 npb = 20 20 mn + 20u mp 4 2222 up
10. 10m tu b + 1. it o + p b. + 12. n nepb ( L 20. 20 men + 21. 22 m + + 22. 22 n+p
d
1. 10 bt ambF1. 2b= 20 20 +21. 2 +22. 2V 18. 11= 26 21 191 20. 22 112 lu
Habemus ergo ex aequationes resolvendas similiter prodibuntaliae sex si velum
efficere arq.. . pro deunt ergo aequationes resolvendae duodecim. literas vero
arbitrarias habemus quidem etiou 12 din spectem, sed vevera pauciores unt quia
ea
itaque remiser
redu ad pauciores reducuntur en enssimenter incraremur
sim Y, V, Z valortu, pro 10 scripsissemus 10+ 10) et in laeteris simedtm incraremur 
praestire non licebit. atbitiarius, et quia
edo copparatitiae, ita in sil
a unam et
t
litiae
abe
eodem redit aquenue quadrato firmulami atbusutcg? quod ea fiet si faciamus.
15 15 ut
ea 1B.)
 itaque potuis aquemus quadrato suoductum exe a + bgy in et fG9, vel quod
atdt coga
y= hn u s ip + _ 1B LXAM, eta + 1A Sxtm, XEP. + I LXF nxIP
y9= 1010 m 1040 X
13. 13 mn
inte
1312 m
1414 m
15aG 
 et quadratum sit a latere lujus quadatoquadhatum assurget
ad. X  rationalem per X) et X per IXam, Xt Et et smiles
Habemus ergo comparationes X, X, X, X, X; et X f quod sunt 5;
et _ ter X. Ju., XI.., X s. quae sunt 9 in summa 14
quadratum autem excitab v0 (= arbusrtcy) excilibimus a latere
D = _ 20 SXIn, XIn +21 Lxim, xip +2t Xtn, Xep
31X
sed ita prodeut
diterae coparatitiae tantum 12, cum nempe 10, 1, 12, 20, 21, 22; 30, 31, 32 m, n, p.
rus 
praestat ergo rem omnem reducere ad Muthplice
sinfimi gradus
aqualitates Et primum quidem quia duas jam habemus aequevalas
qua formulas simplices ut  veluli Xra et x1b, jam simul quadrate aequare
possumu, reducemus Triplices ad lales smplices
Ergo
e
sint X +  X + a y+b, _+c equanda catis. Nam
et ipsum athyu +cist aequare eto huc alibi reduxi.  sint ergo
quadinti vD, ZZ, VY, nempe y+ a = vv y +6 = ZZ et +C= 
sit y = 1aY ( id + AX +2O XX + 2 et eX Lrrm, Nin + 3IHE SXAm, Xrp + aD FX (Xtn, xIp
sit D = 12 tX I Y SIVSLS + C0 AI + UM + 120Y_m n + 13oCXrm Nip + 140 SxtR, X+p
vD =  1I. u2 F 2. 119. u+ X + uD MDXX +Z.  Bu Uxm em + 2 1. prAux Sxemxtp +E. II. 2. NX Exin, rp
2.Ggego Uorzex
210 n. 2 luo
2. 120 2. Margox
sut conparaies ter novem, id est 27. Arbitrariae vero in y, sunt 12, in ipsis V, Z, _, sunt ter quinque seu 15
summa etiam 27. Quod tamen vereor ut sufficiat, quico versih quantitatibus inrationes
ter quol novas lucrate sumus in yuo iolidem prodeunt novi termini
Et ita videtur res laudem futura in rolestate. Ino falso
mminuitur numerus literarum. sed si yfacias 14 +13X + 12X + uX + 10X F 2F ZX Y2OX Nxam pra
et ita porro, lucrabimur in y arbitrarias S,e V, Z, V, in qualibet 4 sunt in summa 17
novae arbitrariae. Sed aequaciones
fiet gy 210. 10 X  1010 in X A 1B. 10 mn + ZIBNIX + EIBAM SKEAN, KAP +E. LBI2 X +Z1AIE N Lnm ip tE Mt enre p Eem Eta
11. 11.
I.ne
s
qu revocando ad  ratiores
geneuliuest
12 p
e
Arb. Req
44 42