DE MOTU GLOBI CIRCA AXEM

610

+ e fin£tang(£ - h) + At vero ef * cof£+fin£ tang(£-$)

aa

= — - ■ - — et cof(£ - h) —---. unde fit e cof£ + e fin£

co LC- h) *

tang(£_ h) = — k, ubi k denotat celeritatem radentem initialem. Quam-obrem elapfo tempore t habebimus celeritatem radentem w = k — 2 $g

( r -f- -^— S ) t, ita ut ea labente tempore uniformiter decrefcat, tandemaa J

ergo certe cvaticfcat, id quod eveniet elapfo tempore t ~ —--—,

e 1 1 v a h (aa+ff)

eritque tum cofA — o et A — 90° — PZO. Quod ergo cum evenerit,videamus quomodo reliquae motus determinationes fe lint habiturae, et

quoniam a$gt —

ank

aa +/

e(aa+/)tang^

erit tangtp —

aak fin^

e (aa -\-ff , -\-aah cof^

« fin^

et tangi

-——-—— , hinc fit a fin s = -■ — —

e C <*a+ff)+aak f hn|

a 4 kk

( 2 aaekcotf

« + - r-zr- +

cof<£>

aa +ff (aa +ff)

e (aa -f- ff) + aak cofg’

erit fin<p =

Cum autem fit

aak fin £(aa+ff)v

(aa + ff) v

r y e -j

, atque hn£ =--- ideoque n

v v

finr?= -. Porro quia efi g cofr — e coff, erit tangx =-

/ f/ eoi f

( vv \

-- + se c.off 2 ), live fubfiituto valore v:

ff J

_ ff ( ee ff + fin f fin + esa 4 finf 2 + ee ( aa + ff ) 2 coff 2 )

* aa +ff ■

ob kk = ee — 2sefCm f fin § + esff fir. f 2 .

COROLL. u

1280. Quo major ergo initio fuerit celeritas radens k, eo diutius mo-tus durat, antequam cefiante fridione ad uniformitatem redigatur. Acfi globus conflet ex materia homogenea, fit aa = fff, ideoque motus ■