200 CAP. VI. INVESTIGATIO MOMENTI

ab(c-b)t* (c-b) % t*

i bbtt + --73-+ -— — tV an (bb -j- ibc + 3 cc ) unde

3 <*

4 an

,1 .. . a{bb + 2bc+ 2 CC ) /-> r a (f£-f sAf + qAA)

oritur intervallum AI=/= —--et CI - __ 1 _Z_ZZ_ i,

4 (AA + A£ + ff) 4(AA+A£ + cr)

Porro ob« 4 = /> 4 +(£-A) 4 / 4

4A 3 (f — A) £ _ 6bb ( c - b)' i tt _ 4 b(c — b ) 3 t i

+ - 73 - + ' ■ ' «

a»

+

erit fu*dt = bH + +

b{c~byt a

na

Cc — A) 4 / ! r n .

4. _i-i- et tacto t = a, fn*dt = $a(b* 4 -b* c±

a 3 en 4 ,, ,,

5 b(c—b)t 4 (c — b) z t*

bbee + Ac 3 +c 4 ), deniqu e.fttimdp — \bbt* + -• +-——»

2ti

5 < 7 rt

= T V n 3 (AA + ^bc + 6cc ).

Ex his colligitur momentum inertiae refpectu axis AC = X V M

A 4 + A 3 £ -|- bbee + bc 3 + e 4

— A M .

A 5

bb -f Ac 4- e e * " A 3 — e 3

at refpeftu axium ad AC in I normalium fit momentum — ^ M.• b *+ b 3 c + bbcc + bc 3 + c * j M,,,, f t?(AA-fjAr+Afr) y(AA+2Ar4-j«) z \

bb + bc + cc 80 \ bb -\- bc+cc (AA+A£-ff£) a y

quae reducitur ad hanc formam:

A* -f A 3 c+bbcc + Ac 3 4 -r 4 , , (b + r) 4 -f- 4 AA£C

A M . -—- - +

(AA + Af+rr) 2

AA + Ac -f ££

C O R O L L. r,

510. Si b = £ prodit cafus cylindri, quo fit AI=r/=|n, mom.inertiae refpetfhi AC = x Mf£, et mom, inertiae refpedlu axium ad illumin 1 normalium = ^ Mff + A Mnn.

C O R O L L. 2.

51 r. SiA=o, prodit cafus coni redii ^ quo fit AI ~f— |n; mo-mentum inertiae refpedlu AC M« et mom, inert. refpectu axium adillum in 1 normalium — A Mcc -f- ¥ 3 o Mna. ut fupra.

C O R O L L 3.

513. Ut omnia momenta refpedu axium per 1 ductorum fiant aequtr-ia , debet efle 4 (A 4 + A 3 r -)- bbee -f- Ac 3 + r 4 ) = aa . ■■ ^ ■■— ^ f . C _

^ bb + hc + cc

ideoque datis bafibus coni truncati, altitudo AC = a , ita debet definiri

_ 4 (AA + Ar + ££) (A 4 4- A 3 £ -f bbee 4- Ac 3 -4- c*)

ut iit aa ----.

(A + f) 4 + ^bbee

EX EM -