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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 190v, page id 00068201:0380
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porro d
et quidem primitivus
quod est quantitas rationalis, quia  e est primitions major linario, adeoue
im (alioqui extractio praeparatoria fieri posset secundum radicem exo
denominatam a divisore ipsius e) ergo e est pax impar ac proinde
p-1 est par ergo e - 1: 2 est integer, adeoque e-1. 2
3,5, 1, 11, 3  19 ete, eritr e-1: 21
hinc si e sit 35i, 
 3 36234 etc itaque
= d, d
et radix extyahemd
in exemplo binomii 22+ S98b cum d sit 2, debet binomium mulbiplicari
per 2 et radix extrarenda sit (ubica, seu e sit 3, debet
binomium multiplicari per 2, ut fiat 44 + 1944, hoc binomium
si extrahile est, habet quod habebit differentiaque quadgalorum partium
8, adeoque ejus radicem  cubicam 2.
Hic jam ostendendum
est. si A si radix est extra hibilis ex binomio, et differentia quada
torum a partibus seu nominibus habet partam unam rationalem, tunc
differentiam quadratorum partium esse ex trahibolem per eandem radicem
Ah Nempe  binomium est a + Nb, quadratorum partium differen
tia est aetaa  b, differut cam nos
sit, radix
binomii quaesitaliux fy ejus quadratum X +g + 2X Hy
cabus ux +3x9 + y+ 3X tus siquadntum ta16Xyg 14X aryly
Generaliter I+m = et (tm = l + C l. m + C. C =1 je- 2 2
1e-1
e
M + C. P- 1. (- 2 jC3
102. 3
M et
ubi posito n esse irrationalem et edigerendo fient duae partes producti, una rationalis  +f. 15
altera irrationalis Rationalis l+ C. C2 1C. 2 M + _. C- p. C2 2. C. 3 je4
1. 2. 3.4
Irrationalis  ( M, C. C. 1. e (Z M, C. x.1. C. 21P. 3.C4 je
Del irrationalis
2.3
Y. 2.5. 4. 5.
5
M
M=6- ad. - f.1. = 14
etc = D = 1b
+ Ce1 e2. et  4 Ct (=D - rb
L12
 M. 
2
e
-2. Z. 4
Jam  bstendendum est O- d quantitatem rationalem dividi posse
aertum
per U l- mm: Quod patet, ex . nam si forimula compendo
loco coefficientium atrobius coincidentium scribantur numeri, fiet
m +14 1C + m + 16je
1
) = l + id 1e -2,
D = m + 12 m: V + 14 M -  (N + iC RCS 16 et
1
horum quadrata si a se invicem subtrahantur, habebium terminos tales
C. m +..  lm P2- md,  nec alipodu nec
e
alii termini oceurrent, horum autem quilibet dividi potest per I=M
itaque O2 = y, vel a -b necessario dividi potest per. 1- m
demonstratdum est  posse radicem e extrahi ex
2  Quod sic consit potest radix labica e extrahi ex
O + D ex constructione,
sed eadem potest extrahi ex O-
nihil enim interest, quam quod ex +M sit- m. Ergo etiam
potest extruci radix ex  jam ex O+ D in C - D fit O-
Ergo extrahi potest cabica radix e ex O- D
et cum
32 - et sit rationalis, etiam e eo- erit rationalis.
Et idem facile patet, etsi ad serem generali serie non expressissene
et 3
jam