DISSERTATIO Vll.

cj6

341. Corollarium 2.

-Ellipfis abit in circulum, fi ejus axes a, b fiant aequales: fi ergo m(239. §.) ponas a“b, obtinebis sequentes exprefliones pro maffa M cor-poris pQq revolutione arcus circularis Qp circa illius tangentem QCgeniti, ejus momento fi refpeftu plani in Q ad QC perpendicularis, etdiftantia ipfius centri gravitatis y a punfto contaftus Q, pro diametros=a circuli, et quavis abfcifla zz=Qa.

Jirz 3 -Z--^-z/(a 2 — 4^

Arc Sin

2 z

a 2 z 2

Q 7;

rz"

ira

24

/(a 2 — 4 Z V +

24

M

242. Corollarium 3.

Maffa vero M corporis pQq revolutione quadrantis Qp circuli circatangentem QC geniti, et diftantia illius centri gravitatis y a punfto con-taftus Q, erit pro femidiametro z — Qa=£a (241. §.)

48

ira 3

Qv-

I 7 a

1 7

4(io+3^

2 (10-}- 3 tt)

. Qa.

b 2 v

a

b*y»

a 1

343, Corollarium 4.

Si ob (Vol. I. §. 550.) loco aequationis ad ellipfim z

h* y (|2yl a a "

fumas aequationem z 2 r=-j- - 2 — ad hyperbolam In (239. §. I.

2 .n.)i obtinebis fequentes formulas pro mafla M corporis pQq revolu-tione arcus pQ hyperbolae circa tangentem QC ad ejus verticem Q ge-niti, illius momento refpectu plani in Q ad QC perpendicularis, etdiftantia Q7 centri gravitatis y a vertice Q.

«M=-|Ta 2 £z4- p — z 2 ez

s - '■ —z 3 e z —

ir

b 2

20ir a 22 b

•ez/(b 2 + 4z*);

- z« z/"(b 2 + 4Z 2 );

Qy:

M

Ints-