CURVARUM»

37 i

Et nota, quod Areae duae aequales, in noviffimis hiice diiobusPRor. ix.Corollariis, jacent ad contrarias partes Ordinatarum. Si area in viif.^' 1 ’*^terutra Curva adjacet abfciffe, area huic aequalis, in alteraCurva, adjacet abfcillae produftae.

CORO L. VII.

Si relatio inter Curvae alicuius Ordinatam, y, Se Abfciffam’ definiatur per aequationem quamvis affedtara hujus formae,'^ Xe +fy r, z s +gy ir z^+byi ,, zi s + 8cc. =zfx k+ly^z*+my zri z" J +&CC. haec fi-^ ra j aflumendo s - x = y z% 8c A = migrat in

fibi aequalem, cujus Abfciffa x, ex data Ordinata v, deter-ebatur per aequationem non affecitam ; y v' xX x e +fv r ‘ + gv 2r) + Lee. | x8ec. j —A = x (").

C O R O L. VIII.

2 ^ relatio inter Curvae alicujus Ordinatam, y, & Abfciffam,

’ definitur per aquationem quamvis affectam hujus formae,^ Xe +fy n z?+gy zr> z^ J r &c. — z®xk+ Iv^z^+my^z 2 * + &cc.

+ z y xp-rtjy"z e + ry 2,1 z- d + &c.

figura, affu mendo s = x = y z s ,

, & y

Sn—a —«

sn—n s>1 —>i

►t s — , ‘ Syi~

v, 8i_y n er s ‘ x s 9. f' — * J * s . Caeterim--

Demon-(per . qua- str atic5Cor. Vili

Ke ... -i -i

kc "EduUarum quartam.) Unde rioviffima in hanc migrabit. 10. y'' s s x s v*. Ex4j ,tetn e t tertia deduftarum efficietur, 11 .y'z^i±v'. Ac proptereaji 2 , 'a 2< z:*' 1 ’’» j^ss 3 "—i» 3 ’’.

h i

^ u i Us inquam aquationem a Newtono pofitam, pro s a , y a , y n z , fubflitunntur earum oef-tles > aquationibus deduftarum 2'. 8 a . et u“ expolita:; et aquatio illa in hanc tranfmuta-ia—« / 3/3

, eodemqiie ufque modo. Jam in nequationem ad cutram, cujus ablcifia z, ordinata

* .f r

x * ‘vuxe-\-fi> , <- s rg-v in -\-bv l ’ , + , — s s x s x i -f InA + mv*’ 1 -f -f [. Utram-

■ v—. y

:‘^v.C l ^ ls aquationis partem dividat quantitas, x s x s 1 X k + lm J- mvm ifj.

/ 3 +^—te

hv

Fiet

^X e +g v z ” + 1 X k + h>" + + j ” 1 - a' ' . Hoc eft,

per aequatio*

dedr,

<l fN . u &arum 6 ’’’. s A v 1 x e+fv'+gv 2 ’' + £x ' i ’ 1 + ,| x -f lv n + mv 2n -f) 1 — x x . Hujus

I «X v -

— v X

\Pars utraque evehatur ad gradum illum cujus index quantitas *; fiet

X k+h>" +m v™ + ^~ X - a-. QiE. D.

Bbb a

migrat