46 r

CAPUT II. DE MOTU

fitus cujusque elementi in flatu initiali inore solito determinabitur. 5eM«per autem ex natura trianguli Sphaerici ABC erit cof^ 2 + cof»; 2 + coO as= i; praeterea vero ex sphaerici; notentur sequente; determinationes

cofBAZ —

finBAZ —

cof»

: cofABZ =

fin<?

co

ii

cofA

fin ABZ =

su>t/coi A

cofBCZ —

fin BCZ =

co Cq

h

cof£

fin a

fin ^ ' fin Yf

Porro vero erit

cofZcofjj - nrT _ cof>j cofS’ r cos? cofA

cofAZB = - cofBZC = — f -x 5 cofCZA = - —

fin£ (in»j itn jj ImZ- lni£ fiuI

fm AZB = + ; fin BZC = + ~~ ~~ i ^ CZA ^

iin£ linjj ltn>j linZ- im£ hnH

993. His pro flatu initiali definitis confideremus flatum corporis, inquo elapfo tempore t reperietur; ac primo quidem in quemcunque lo-cum centrum I fuerit translatum , quandoquidem ejus determinatio nulladifficultate laborat, ejus locus cogitatione faltem in putidum 1 transferatur,fimulqtie cum eo totum corpus, motu fcilieet fibi parallelo. Et quoniamin fitu translato femper datur talis radius, cujus diredio eadem cfl atque i»flatu initiali, fit 0 in superficie sphaerica id pundttm, quod tam in flatuinitiali quam in translato pofl tempus t c-undem locum occupat, ita ut ra-dius eandem diredionem obtineat pro utroque corporis flatu. Pro ejusergo fi tu ducantur ad angulos arcus OA, OB et OC, qui vocentur OA — «,OB = /3 et OC = y, quos ergo tanquam certas fundiones temporis t fpe*dari oportet, atque ex his nancifcemur fequentes determinationes:

cofOAB =

fin 0 AB =

eof/Z

lin«cof y

fin "

; cofABO —: fin ABO =s

coi

«

«

fiujZ

coi y

Ii n /3

cofBCO =

cof/3

fiaBCO =

itu ycof«

fin v

Porro vero erit

cof« cof /3 cof /3 cofy cof« cofy

cofAOB = - -cofBOC=- -----—; cofCOA=- -—-JL

1111 oc (111 /3 Im^Diiny fin« finy

„ cofy „ cof« „ cof/3

fin AOB - - - Y —; fin BOC - - -; fin COA _- -f-.

fin « fin /3 . fin /3 finy fin «finy

Insuper vero erit ut ante cof«* -f- cof/ 3 1 -f cofy* = 1.

993 ' ■