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XLVI. Problems by Edward Waring, M. A. 
and Lucafian ProfeJTor of Mathematics in 
the Univerfity of Cambridge, F. R. S, 
PRO. 
Nvenire, quot radices impoffibiles 
habet data biquadratica aequatio 
a: 4 4- qx z — rx 4- s— o . 
l mo Sit 256 s 3 — 128 q* P 4- 144 r z q -\- 16 q 4 X * — 
27 r 4 — 4 r 1 q 2 negativa quantitas, & duas & non 
plures impoffibiles radices habet data aequatio. 
2 do Sit affirmativa quantitas, & vel — q vel q — 4 s 
negativa quantitas, & datae aequationis quatuor radices 
erunt impoffibiles. 
3 tio . Sit nihilo aequalis, & vel — q vel q z — 4 s 
negativa quantitas, & datae aequationis duae inasquales 
radicis erunt impoffibiles. 
2. I nvenire, quot radices impoffibiles habet data 
aequatio x 3 -\-q x 3 — r x 1 -\-sx — tz=. o. 
i mo Si figna terminorum aequationis w'°4- 10 q w 9 
4- 3 Q q 1 4- 10 5 X w 8 4 - 8 o ^4-50 ^^4-25 r X W 4- 
gs V -^r 124 95 **4-9 2 + 200 r; X ‘w 6 4- 
66 q ; - — 360 q s-y 19 6 q< s-\- 1 iti g~ r 4-260^54-625 
?4- 4 oo y 71 xw s 4 - 25/ 4-40 P— 53 r 4 + 5 2 ? 3r — ‘ 
522 ^ / 4- 194 <? 4 54-7 08 4-, 240 q z r t 4- 1750 
y r — 5 r t X ‘t# 4 4 ~ 4 Q 4 - iq 6 -S’ — k° ? J 3 °^ 
j* — ■ 02 y r 4 — 7 y 4 r a 4- 370 r 4 5*4-612 q~ r~ s 4-700 
r 1 / — / a j 4, 2500 Py'4- 80 r t q 3 — 2150 qrst 
Xw 3 4-400 s ' — 360 q 5’-— -i 5 5 ,+ 5 4* 2 4 ^ ^ ; 
— 45 
Read April 21, 1 
i7 6 3- J 
I. 
