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# Title: Leibniz-Handschriften zur Mathematik LH 35, 3 A 21
# Folio 4r, page id 00068234:0007
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Aequationem Solidam quamvis constrnere
oper ope Circuli et Hyperbolae aequilaterae datae
sit ex aequ  a +by aequatio ad Hyperbolam
sit X+ y + CX + du aequ. 0. aequatio ad Circulum
et
(4)
X aequ + a + b per aequ. 1. X aequ a + 2ab + b2
fiet in aequ. 2. a 4 2aeb + b2 + yt q RaC + bc + dy aequ. 0
Unde: y + dy + b y + 2 a b y + at aequ. 0.
+ bc. + ac.
Sit jam aequatio data solida qualiscunque
+ Ry alquy abr y +lis aequ. 0.
(9
(10) 2
(1) ra - 2b
fiet daqu. p. a aequi A 2btc aequ re seu Cxequ g.
(12)
(13
rusus C aequ ag - b aequ qu - b. Ergo b - b aequ. qu
52
454
(16) 
sb
454
(17
 s
rae +sqaa
et 1 = ra aqu a Traetsq seu baego a trat sq + ra
2521
25
Sed huc generalius hoo modo:
252
y X aequ. +a+ by ad Hyperbolam aequilateram
X + y + CX + dy aequ. e ad circulum
X ago a + b x ago at + 2 + B
a + 24b + b + y, + ca + bc, + dy aequ. e ex aequ. 2.
y4 + dy3 b y + 2a b y + at aequ.0.
+ bc. 4 ca.
et.
+ p y3 + 9 yt + r y +s aequ. 0.
Ad huc generalius
yX aequ ax +b X. Xaequ d Z v aequ a + v
X aego Y +a. seu yx + bx aequ cy + ac
+ 6
yX L ax + by + c
X aego y+a X aequ  + 2ay+ a
(3) 3 +b
y2 + 2by + b2
2
X + y + dx + ey + f aequ. 0. fiei Cy 42ay+a + y + cdy + acd +ey+f +
y+ 2by + b
y + b
seu cy + 24Cy +ac + y + 2by + by, + cdy + acdy + bedy + abcd
+ ey3+ 2bey + b ey + fy + 2bfy + bf2 aequ. 0
4 + 2by3 + c y + 2ac y + ac aequ. 0
+
Ponatur S70. et a
e...
+ b
+ cd.
+2be.
+fr.
+ a cd. + abcd
+ bcd. + Bf2
+ bre
+2bf. arbitrariae 2 ac. c. b. d. C. f2
quo
fies
y
+ 2b y
ue