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# Title: Leibniz-Handschriften zur Mathematik LH 35, 14, 1
# Folio 120r, page id 00068201:0239
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radiae a velut termino primo
duplam
btrahatur
(ad summe additur)
si Te quantituli Cuidam, alia bper prirrs divisa addatur et a summa subtrahatur terminus
resivnum adu
a residuo ruisus subtratatur terminus quartus si qui sit quadratum tertii a praece
dentrum terminorum duplodivisum; atque ita porro vi infinitum continuatus intelliga
tur processus: Summa serici hujus infinite aequabitur Radici quadratae bnonu
Resui) ex termino quadrato ter quantitaties primo assumtae a, quadrato, et altera
quantitate b composit seu  Sa +b (= a b
si hoc apperietur aderientum cujus natum va a- X Y. fiet:
a-
X +
2a 5a =2
quaeanda equatio
initio acta
sire
porro
188aGa- X = X 
X - y. Ego N =- ay aly: = a + a Xa
aXa ay +X Xay = ay+ a . Ergo
ay+X = saeyt ay
seu adx = Sae ayty-ay
2a + b, (5, 4, + b + 2a +b 4 b+ 64a, 2a + b
e
2ta s priores radice, duplas.
1uel 2arb, 2. rarb + b 9
v
2a+6,
ba 2a +b, C2a + b, 2 va 2a +_
2a + bea + b 2a + b, 2ba
s
a 44a + 4ab +62 2a +b cub) 2, + b 2a +b, y sa
2ia 2a + b
jam  +B,. O, - 8, et 0= 4
Ergo fiet Z + D, = y = 4 hic Z + 4-
er
sive cee ergo operationem tandem ita in compendium
5
reductam, nempe, Residuum oprationis praecedentis appellet 
sunt
duplum Radicis appelletur D. Eadix nova = O erit = Z. residuum
novum e C seu radicis novae quadratum seu dvidendus secunda
secunda radixD
Et quia prima Y est b, Eit ergo prima radix
tertia
et secunda radix erit
a
ax
ox ter
oe
2a +b, 23 n 
+
20
s
Circulo symmetros eo
potestas statim aib
4a B, 
+
ry. 2)
t.
2, 4y 6,
b1. 2y,+-
13
2
27
166
1984 4
22
+ sia
228
+ 386,
8 t
A
198
14q2
um
158 fiet 31984
6.
6 3838-
353
38, 1C, +,
1442)
81Z
38.= 5926 38∞ 2
188
2a +b
ac
456 f228126
3= 388, 386
certis
get resionum prum
2
) D= i
et quarta erit
+43
vite at trus
229+3
-
23 89+ 47