CURVARUM.

373

tatis extrahi poffit, cujus index eft w; vel etiam ponendo 1, Frop -, ix -^ X=:i= T = a= 7 r , ut alios caius praeteream. Co *' X ’

CORO L. X.

J^o e& + f z v + r ‘ + gz' +u + &c. vez'— 1 + y + r\f z v+ ”~ 1 + v + ^rgz i+2r> ~ 1 + & c .b+te^+mz 271 + 8ec. et f i lz v> ~ l + ir\mz lr ‘~ l + Lee. feribantur r, r, s, 8eJ tefpedtive ; 8e Curva omnis cujus Ordinata eft nsr+QRSx k ? '~ , s u ~ 1Xflrwl“(nHn), fi fit r=a?=l = * - T - = 7 , *=?=$, & rV=

migrat in aliam fidi aequalem, cujus Ordinata eft x^x a + bx 'H(”") Et nota, quod Ordinata prior evadit fimplicior, ponendo unitates

pro

(") Ostendimus quod Nevvtonus dicit hoc modo. _ Demon*

Hk funt aquationes a Newtono polit* i. Grrxv. 2. x — ez + + »e "t'*’ 1 + , [ T . 3. a — —. V R ^I !7

77 vOR« iA^.

4 - H Ponantur praeterea, 5. vr+ »"+ rjfz” + » +2 * Ijs 2 ’’ + ,| — r. 6. ,

T_—-_

7. ? + y a »+» +<?z >+ 2 ’’ + j - V. 8 . + J = r. .

Ex his aquationibus hx alix deducentur.

1. x — E’ 1 (ex 2 a & 7 3 politarum) Ergo. 2.

— E. 3. L — ri (per 7 m et 8 m polita-

r Um) 4. s — - (ex texta et septima pohtarum) Ex h.lc autem, et ea qu* primum deducebatur,

v eniet 5. s — x * s— v.

Dat* autem curva- Ordinata iignideabitur hoc fymbolo; n-z 5-1 x R X s x ~ 1 x a + 3 £~] M . .Curva- tranfmutatx, cujus abscissa v.-, Ordinata deiignetur liteni O.

Erit igitur x : z — 1 X R X s X—1 X a + ^1" : O. Sed (per aqu ationem 2 m & 3^ deduUa-

£u ®) efficitur x : z = r : —--Ergo u-x 5-1 X R X s x ~ J X a + &F] “ ; O =r : —. Ergo ;

7T—J . <T Sw—I b

TTi

Q :r ? X R X _s_x^r+toF)*. Sed (per aequationem dcdu&arum quintam) s. x ~~ l z=.

^ *

z v—Xv. Et (per xquationem deduUarum primam) E® 1 — a- . Quare —I —

z> — 1 x' J x R

* w z v—XV — 5 (per xquationes politarum 4 m & I m ). Hinc 0 _ ---X»Hj".

S

x xr

5 td

X R - r (per aquationes quintam et oflavam politarum). Ergo o -

^ + ivj” — x 2 X a + l s - K Sed X T =r x * (per aquationem dedu&arum primam) — x : (per^Uationem politarum tertiam). Ergo Or x 3 x a \ . Q^E. D.

("’"') Stewarti emendationem fequor. Editiones ipfius priores habuere «s + £r t ]‘' ; vitiofe. ,

("") Hujus Corollarii veritatem cum Stewarto lic often limus.

Ei* funt aquationes a Ne-.vtono pofitse.

^ + 7 v+^]+, - R. **