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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 268r, page id 00068201:0535
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man
M n . Cm abn +d, multiplicane per quantitatem, in qua M, et n non
extent nisi dato gradu praeditae, e _ eodemque modo affectae, sint autem d. data, at c. et n. quaesitae.
cM + b n + d in em + fn + 9, fiet: ec m + eb mn +gcm +gbn +gd
fb n +fc
+de +df
fiat ec + fb. sive b, eC. rursus eb 1- fc sive b, = fe et Quod non
procedit nisi f sit quantitas impossibilis, Unde etiam b fier impossibilis sed si omissis terminis
m. n. reliquos examinemus, eb + ferjo sive b pp FC et gc + depjo. sue epp- de,
et 9b + dfB0. sive bp = dt - FE sive ess ed fiet rursus absundtum,.
sit  b m +Cn + emn + d. Ho. ita multiplicanda ut prodeat qu mn vel mn, vel mn,
aequalis datae quantitati hoc se ipso praestabitur. Ponendo b et c 10.
Sit bm +n +v, + fmn + quiv + huv + d 1o multiplicanda per totformulam talem, ut
in producto tantum restet mn + M V +n  Sed hoc iredo impossibiet
si essent equationes nn  mv + ntv t9. mv FY
m+ n v S.
foret m + q md + rM + s 10. Et componeretur radio una aequationis quadra.
ticae, ex tribus radicibus aequationis cubicae  Haec si succederent valde commoda forent
 sed non video quomodo facile succedere possint. Habemus quidem aequationem m +n v
et mux  datae, unde fieri potest mr v  Y. Sed habemus, mn+ mo +nvri datae, ut 4.
quod turbat
X X qX + rno. XH 1O Y + tXF4 + 1O 7- Y +
Sro x ponatur y + p. fiet y +3p V + 3pE V + p B sit data aequalio; y + b st +Cy + d  o. conferatur
inventae, fiert  PB) b et q c - .
c
4 1
+ qu
ir  e r  4.  + B ⊓ d + 2, b e
d + 4 db7 - 2 dcb, + 4 b6 = 4 b + c262
4, 27
42727
27H  - 3, c, b + 3C b+ - b0
Ergo Y + q
sive distincte scribendo:
27, 3
27,9
X + 2, H
27, 27
 + d
4, 27,3
4,9
= dch,  cb, + es d + db- 8. eb +0
27
9,2
27
Si alsit C,  sive aninus pemultimus in data, fier y ( _  + B +  Ae aB + s = + B -) , db
relictis autem omnibus fiet VF 13) = d - cb + b
Povamus jam b,22 Cr 2- 4)
de - p
2n + Y = B d- .b + db3 +c
36 2t
0b7
=R, 823
-362
et =H = R (+9823, - 22) + 224)
 2
27
ber  42, 2-885165
debR 2 - 2R 4)
+E, 1 2, - 3, 427 + 3. 1652
27 Si
t
= k + 25. 22+ a)
4 27
Data aequatione quadrato quadratica, ut quam simplicissima
habeatur irrationatium expressio utile erit tolli terminum
X + rX +s B sit XH X + b.
fier: yt + 4b y3 +6b2y + 4bY + b4 +0. Unde ut selent
p. .. + 3pbe. +3pb. + p b
1296. + 96
lenminus fiab
negativus, erit
ec 6b2 3pbr
+ Pb +
2P
16
Ita enim statim redinet
ad (ubicam, secundo bumco
carentem resula Huddemi
se lertium X + pX.
1
erit  - +