369

Cor. III &IV.

CURVARUM. '

Ponendo-^ = /, & z s = x, migrat in aliam fibi aequalem, cujus Or-P/oiu rx.^nata eftd#~rx e+fx' 1 +gx 2v + eccc] x ( ss ).

C O R O L. III.

.J^-Curva omnis, cujus Ordinata eft z^~~ l x a + bz^ + cz' 1 * + &cc.

Xe+ fz v, +jrz z * + &c.h, aflumendo quantitatem quamvis pro r, &

Ponendo — = s f 8c z s =x, migrat in aliam libi aequalem, cujus Or-at »9 —1 _ _

^aeftd-# -- x a+bx^ + cx^ + f&c. x e+fx^+gx 2 " + &c.|\

C O R O L. IV.

^Curva omnis, cujus Ordinata eft s 9 ~ r x a + bz^ + cz 2 ” + 8ec.je+ fz*+oz 2 «+ 8cc.j A x k+lz*+mz zn + &cT]“, aflumendo quantita-quamvis pro y, 8c ponendo — = s, Sc z s = x, migrat in aliam

v§—»r

^b'

1 Aqualem cujus Ordinata eft — x~ x a + bx* + cx z ’ + &c.e +fxF+gx 2 ' , + &c.] x x k + lx’ + mx zv + &c!^.

IV. o-

01 R ex quatuor conflet nominibus, s ex duobus.

B

*-E _ ___

6 + 3 An +f*r\!>I

(q' ) Dummodo fimul a nihilo generari inceperint. Aliter enim 1 altera altera dato major erite °nietr. Flux. Prop. n.) Arearum autem partes limul genitas vel fic etiam aequales erunt.

— 6 -f- hr, \fk g — 6 + 2^ri\gk — 9 -j- jAr, \hk ^

— 8 + pr.lr/ — 6 + — 0 + 2A» \tJ-rt \gl

Vid e

Geometr. Analyt. Prop. vin.

( SS)

^>Ul

Ruatur enim z 1 Xe+fz' +gz 2 ’ 1 + ) x , ~y, et fit v Ordinata, a Abfcifla curvae cujuf-

Abfciflarum

Demon-

stratio

■git^j, Cu J Us Area area; alterius, cujus Ordinata fit^i Abfcifia z, femper fit aequalis.

£. , Axiones "inverfas Ordinatarum inter fe proportiones gerunt (ex hac Prop.) Hoc eft Coxali'" v Q. Sed propter z s = v, erit i — sz~ 'i. Quare v :y — k : — i ; s&~ 1 .

fe — — z~ s X e + /V’ + Sed propter - =r s, erit 3 rr —. Et

JZ 1 S ' * S n

yQ _ »'—

- V ,J . Et^rrr- zz.v 9 .

feiYw 1 y vy

°Pter — • "* - 3__;

^ ^ -v, ei'it L rr x s , et “ *• * rr .r **, et z “ x

^2>, T - -s

° ** ? ’ , , tn>) wv ° — 5 , r >i ,,, K

— A ; z> —x 3 ;■%■)(■ vf ; z = x . Quare — z x <r + fz 1 -}- p- a z 1 q- , r — <o ~

s * ' o ' 9 1

Si:

* <7 +/* , +.?.v 2, + ,j\ Q.E.D.

hujus Corollarii demonflrationem in commentariis fuis Stewartus attulit,

V

°L. I.

B b b

G O R O L.