DE CENTR VIR. OSCILL. ET GRAV. 211 



proce proportionales runtvelocitatibus. His ita difpo- 

 fitis, fmtcorpora in fitu M et N quocunque: fitque GH 

 perpendicularis nd MN ; fiKflis parallelogrammisBGLK 

 et BHIK, dudisque diagonalibus BL etBI , patet has 

 iplas diagonales exprimere polfe velocitates corporum 

 M et Nex vtroque motu refultantes-jhincquc \im viuam 

 corporis Mexprimendam efle per BL ^ xBN feu BL ^ xBH 

 et vimviuamalterius corporis perBI^xBM fcuBI^xBG: 

 vnde demonftrandum reftat effe BL - x BH-i-BI ^ x BG 

 conflantis magnitudinis. Per centrum B ducatur QR 

 perpendicularis ad HI et ad producflamGL^fic eritBL^ 

 -:rBG'^-BK--f-2GRxBK,atqueBl2=:BH^-f-BK^- 

 2HQxBK , vnde BL ' xBH+BI ' xBG = (BG - x BH-f- 

 BK'xBH-h2GRxBKxBH)-|-(BH'xBG-|-BK2xBG- 

 2HQxBKxBG). Suntautem in quantitatibus parenthe- 

 fibus inclufis duo vltimi termini aequales , quia GRxBH 

 nrHQxBG; efl itaque fumma virium viuarum ex motu 

 compofitooriunda:=:(BG^^-BK-)xBH-HBH^-hBK-) 

 xBG ; et confequenter in omni fitu eadem, quod erat 

 primo ioco demonftrandum Nunc fi \'terque motus 

 fingulatim confideretur , habetur vis viua motus rotato- 

 rii pro corpore MzzBG^xBHet pro corpore NzzBH^ 

 xBG et denique vis viua alterius motus n:BK"x (BH-f- 

 BG), ergo fumma virium viuarum ex vtroque motu fed 

 non compofito oriundair:BG^xBH-f-BH-xBG-|-BK- 

 x(BH-4-BG)z=(BG-H-BK-)xBH-i-(BH--f-BK = ) 

 X BG ,ergo eadem quac ante:quod erat fecundo loco de- 

 monftrandum. 



D d 2 V. C(?. 



