421
.V X' X i A'“ , ^ O
# +-1-—j-t—;■!—/ : ^ c '
a 20 . 2 a> •>'’ ^
% +- 2 - + -
20
^■4
x
zci*
X*
*
*
*
X XX
r +— + ^
a za
za
x'
+ “l + “s &c *‘zar za?
..4 v 5
* + — ^-- ^-5 &c *'
a 207 za^
*• *
—T "f-"s ^ C *'
07 za*
x $
* +— &c-
a*
ANALYTICA.
c io. Iterumque } x s in marginalium terminorum valores adfcito, Inventio^ Proxime deprefiiflimis f ad Se - x\ in unum aggregatis, elicio dm?*”" quartum terminum valoris y- Et Ec in infinitum.
47 - Exempl. 2. Ad eundem modum, fi relationem inter x 8 c•h habita aequatione ^ = i + -E + ;p + ;/ + / ^~ c ‘ CU J US termino-rum feries infinite progredi fub-intelligitur, determinare opor-tet; pono i in capite, reliquoiqueterminos in finiftra columna, etopus deinde profequor pro moreadjundi diagrammatis.
Ubi propofitum eft mihi eli-cere valorem y adufque fex di-menfiones x ; et ea de causa ter-minos omnes, quos propofito ni-hil conducere praevideo, interoperandum miftos facio; ficut^tnuit nota 8ec. quam feriebus interdiis adnexui.
4^. Exempl. 3.. Pari methodo fi proponitur aequatio 4 = ~$x
+ 3 xy+yy-xyy+y 3 —xy 3 +y 4 -xy 4 &c. + 6 x 2 y- 6 x 2 + 8 x 3 y— 8 x 3 +1 oxy~lo ^ 4 + i2x s y-nx s 8ec. et valorem y ad ufque feptem di-^enhones x eruere inftitutu-m eft, terminos, ut in adjundo^grammate, in ordinem redigo, et operor ficut in praeceden-hbus; hoc tantum excepto, quod cum hic, in finiftra colum-y non tantum unius, fed etiam duarum ac trium dimcnfi-°^Um exiftit, vel etiam plurium, prout valorem y ultra gradumExtrahere ftatuam ; fubjicio quadratum et cubum valoris y eate-
nus gradatim pro-
2X* C.t 4 2X S
-1 -!---+ —
^ ^ 2^ a i
&c.
20 20 '
X J X"
2 +--/-7&C.
20 20 T 2a>
3 Xy
+
+ 6V+ 8^+ K
X y 4 *
— $X -
- bx z
- kU 3 -
IOV 4
— I2X f — I 42 6
&c.
y
2
y
*
*
- J * 3 -
6 a - 4
_ 7 S p5 473/1
J •* . t» ^
&c.
*
*
* -
gx*
- i 2 A- s -
&c.
V
*
*
*
— 12^5 — 16 .V 6
&c.
■d & c .
#■
*
*
-*
— 1 /’
&c.
*
*
H +
9 x4
+ 6 ^ 5 +±?Lv 6
&c.
*
*
*
*
■* -|^ 5 - 6 * h
&c.
&C.
*
*
*
*
* -y- h
*ma
- 3- v -
6x z -
i 5 2-3- V
x 4 —
3 3 3 y.5 _ 3^7 ,-S
c ^ ) _ 2 5j.4 __ 9 I -v«) _ II lj.fi .
+ 6x s + &c.
- V-v 6 3rc.
zyyx" 1 &tc.
ductum, ut cum invaloribus marginali-um terminorumdex-trorfum gradibus in-fcribuntur, terminitot dimenfionum e-mergant, quot ad fe-quentem operatio-nem!