aV C? V 3 n
— - -4 + -4 8tc. - 2SX + X
•* 2 X
A N A L Y T I C A.
2 x 3
477
&C. + 2# 1 V-Af + — &C.
De Areis
3« Hyperboli--
26.. Ad eundem modum ab, feu x, pro definita linea adhiberi CIS '
.4
Z?£j
x|
_ ay
x\
cfy*
cfy 1 y
X + 1 x* + pf + 4 X«
&c.
potuit, et fic prodiiffet
27. Quinetiam fi bifecetur bB in c, et affumatur ac effe de-• finitas longitudinis, et c b ac cb indefinitae: tum di6to AC-e, .
&c.
. , . , 7 aa s s \ aa aay a 1 y z a 1 y* tfy*
et cb vel CB=y, erit bd- —— () - — + -j +'— + — +
e ’
A,,3
Indeque area hyperbolica parti bafis bc adjacens y + yr + +
a y* 0 . aa
8cc.. Erit etiam cb — ——
4- e+J
aa _ *x + a x _ fZ + fX & c . Et
inde area alteri bafis parti cb adjacens
e 3
a y a y
, + -r “ fr + -4- &c.
e 2S
Et harum arearum fumraa — + &c. valebit
e zs $e
a y
ay
28. Sic aequatione z^ + z z +z-x 3 = o, ad Curvam exifl
aa\
x|
aa\
x\
ente, ejus
radix erit z=x-\- — + (0 &c. Unde fit z~jX 2 -jX~
qx 812" 729V
y-
-2-&c. Et area £dbJ=|x j
LiA 2187^ 2
+T^+ — +
7
&c. hoc eft,
■i y 2 __L y,2 X 3X
81X
’|9X|
8ec.
7 Qrp _ Lv 2, _
:x- + Y x+ y- ■.
2 3 Sia:
j9^r| Sia 1
8tc. ±1 8cc*
9« 27^ 35^
29. Poteft autem terminus ifte hyperbolicus; commode devi- ,tari, mutando initium bafis ; id eft, augendo vel minuendo eam >per datam aliquam quantitatem. Quemadmodum in exemplo ,- -f, erat aequatio ad Curvam ; li faciam A effe .*
CtX —X
priore, ubi
mitium bafis, et fingens Ab cujuflibet effe determinatae longitu- -^inis, puta -i<2, pro bafis refiduo, Ab, jam feribam x : hoc eft, fi *diminuam bafem per feribendo x + ~a pro x; evadet -y
-z, et per divifionem z=ja- 2 d x +
4 a' + 2ax + x
&c. Unde fit z~%ax-
fx' i + 1221. Lee. - arete bdv>B.
^ 81«
Et ftc pro initio bafis adhibendo aliud, atque aliud ejus punc-tnm, poteft areacujufvis Curvae modis infinitis exprimi. ,
30. Potuit etiam aequatio
(£) Vide Cap. m. § 13. •
ax +
:s', in duas feries infinitas re-
iclvi