CENTRUM INERTIAE IN IPSORUM &c. 553

q (d$- + d<p) fin(^t — v) -s- -—At linC/w — v) cof(| — A) = »

feu q (aiZ- + d(p') + dt cof(£ — &) = o. Deinde II. fin (4 -j- A

aa

2 (f/p

T (p) — III. W/W + & + 9) dat Aq Cm(fx— d)- dt fin

— r) fin (| — B) = 0 feu Aq — ■ • dt fin (| — A) qui valor in ulti-

aa

tua aequatione pro viribus vivis . fubfiitutus praebet xdx -f ydy -p zdz — qdqiiincque xx + yy -q- 22 = 88 — Conft. + qq = Conii. + 88 fin/ zita ut fit 88 eof/ z = conii, ut jam invenimus ob 8 cof/ — p — h. Hincillas habemus aequationes a litteris l, m, n, A> p, v imnnmes:

I. q (AB + d$) + — dt cof(Z - A) - o ; II. rh - -^Laa aa

dt fin(| — B)

III. dv — 2 $gdt cof£ ; IV, vd(p — i^gdt fin|

quibus adjungatur haec finita tang£ = ——--— , quae transformata

v - fqfmB

in hanc v fin £ — fq cof(g — A) — 0 , ditlerentictur dv fin ^ -J- vdf cof£

— fdq tofC| - 3) + fqd£ fin (| - $) -fqdB fin (5 - B) =p o. lamI. fin ^ — •&) + II. co'I\| - B) dat q [AQ- + dtp) fin(| _ B) + dq cof(|

— A) — o quae per / multiplicata illi addatur dv fin| + vd£ colf + )q

(dt + d(p) fin(£ - B) — 0 . Porro ob , erit v (d(h

vdip fin £ r

+ d|) cof£ + fq {d£ + A<p) fin (£ — B) = o feu (rf<£> -f «?£) (y cof£ -s- fqfin (| _ St)) = o quorum fatlorum finitus v cof£ + fq fin(£ - A) C va-ueicere nequit, ob v fin£ — fq cof(g — A) — o, fcqueretur enim indev co!A =co, et fq cofA — o; quod nonnifi cafu B = yo° locum habet,Relinquitur ergo ut fit d(p + dj* = 0 ideoque <p -f £ = Conii.

Hic impetrato reliqua non difficulter expedientur; ad integrationesautem determinandas pro (latu initiali t = o, ponamus fuiffie celeritatemprogreffivam v = e, ang. ^ — o ; ang. PZO = A = h, arcum ZO = s= f; et celeritatem angularem 8 — k in fenlum ACB ; hineque p — h

— r rr „ „ „ sf fwf cofh

— 8 coi / = 5 coi f, et q = e fin f J porro tang^ — —:----—.

e — sf fin f fin f)Statu-

Aa aa