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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 191r, page id 00068201:0381
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M=6- ad. - f.1. = 14
etc = D = 1b
superest land ut
aextrahendum
 Hac jum praeparatione facta, ut habeatur binomium
carens gractionibus habens unam partem rationalem,
et tale ut et ambas tales, ut differentia quadratorum
ejus sit extrahibilis posito denique extrahendae radicis
exponentem esse primitivum (alioqui praeextractionibus eo
reduci potest) jam modus ipse extruhendi est ab solvendus.
Hunc aat secundum Cartesiam schotenius proponit talem
quaeratur numerus rationalis radice quaesita a + rb pauto
major, ut differentia non sit major quam ,, quod per
communem Aaithmeticam facile haberi potest, is numerus
vocetur N. hunc addatur radii differentiae quadralorum
partium  divisa per N, eritue jam fint N 
jam fint N + B. D jam funt N4+ aa b
Ta
jam fiat. N +- aa - b ajo si extractio est
possibilis maximum numerum integium rationalem
in hoc contentum esse partem rationalem radicis 
radicis quaesitae sul. Nam pro N substimamus
veram incognitam qua radicem qua est (+ m et
ZC in
demonstro: Iaa-b = 10-  = VO+D. ese- D
jam O + D = l+m et (0 -D = 1 - m: ergo fiet
Vaa -b = U= mm ergo habemus A m + d -nm = l
e
2. ltm
seu l+m +. l- m = l. quod constat
Harc quidem per ingeniose ex cogitita sunt, qu sed
non salis faciunt, quando agitur de extrahenda radice ex
binomio absurd impossibili
.
sit exemplum
quaeritur. 31 + f-1. Manifestum est hanc quan-
litatem nunquam posse dari solam, sed semper dabitur
simul et
us
1 VI - f1 vel aliqua ei aequi valeris
ergo si porro differentia quad ratorum partium est 1 - - seu 111 se 2
ergo multiplicandu est irration binomium per 2. jam quia
et fiet 2+ V-4, cujus differentia quadhalorum partium est 8.
itaque pars ipsius radicis est rationalis integra jam set arb-
a+ b jam B set C+d = C+ e e
el 95+g = f +f  + CC, C2 2,
1. 2.S
GdF + c. e1
. 2
L3s rg = Ys + e fist
e.- et Ego fiet
1. 2.3
q’eu
.9.5 + C. C1. C25 g: 5 et
1. 2. 3
Cun adde (3 (+ F.gdestratur g quantitus ingpusibilis renanente g, s, ete et nuet numerus, qui est
et
Al 13.1s-1
31.1-1
+1 + -1
24 + Y-1
3+ 3. L Y.C
221 -1 V-1
is
H +3. 1. Y- 3
3131 
0