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The properties of Lines of the second kind. 
I. Put Aa — d—2AC — 2t\ hO ~ *~2BC ~1C j AVt—2p\ PD ~y j CD—*; AD = 
— i f, 
Then pd =Cxad(7. 
Or x a x j- x ± tt ^xx—dzptqpf- x 1 ' 
7=r. 
-- 4 -M-r-P 
For pd 
AM X A D AQJC Da 
(by fim. As). Th. pd‘=— x ADa. 
MK a a a a 
2. Confequently —yy — ±tt=pxx—duzpuu = dzldd=p xx. 
P 
3. Hence —yj—r^xx—t^uxii—xu. 
P 
4. And pt—cc , or 2pd —$$ •, for when y~c~ fj, then x = c. 
5. Therefore * ~ p ** 
ad« cfc/rqp** 
</</ » 4/4/ r/ 
AC 
6. The curve line whofe property is yy-{-~uu — zpu — o, 
(where the abfcifia begins at the curve), 
Or yy- {-—xx — cc— o, (where it begins at the center). 
is called an Eilipfis. This curve returns into itfelf. For when x~o^ then y — 
and when yr=o, then xzzt. Which can happen but two ways. 
7. The curve line whofe property is yy — ^-uu—zpu — Qy 
Or yy — —xx-\-cc — 0) is called an Hyperbola. This curve fpreads out infinite 
For y increafes as x increafes ; and has four legs tending contrary ways: for xx, 
yy , may be produced as well from — *, or — y j as from -J-*, or -\-y. 
8. If the point a, is fuppofed to be at an infinite diftance from a, fo that a ru 
a? moves in a parallel pontion to ad; then is yy — 2pu, or yy— 2pu~o i the prope 
of the curve defcribcd, and is called a Parabola. This curve fpreads out infinite! 
/or y increafes as u increafes. 
9. I 
