25» JDE DENSITATE METALLORVM 



t.illo III. P:c — 3:"; funt crgo omncs h.ie trc5 iactiirac 

 fimul fiimt.ie "-^— p'"^'^^ acqiuilcs iidiiriic mixti /) ; vnde 

 prodit :ic,|iutio pnma talis , ax-\-by-{-cz — Vp. In 

 fliiido autcm N paritcr clt pro metallo I, V: a^x -.^^ 

 pro metallo II. P : (3 rz j' : ^^ ; pro mctillo III. P:y 

 inz: p- ; vnde axlcm inrc fict aeqiiatio lcciinda a.v-H 

 f3 >• H- yszi: Ptt ; tcrtia autcm acquatio (iia Ipontc ttuir, 

 nempc .v-|-^' H-^— P; 'gifin' cx his tnbus ac(]U:'.iionil)Uij 

 trcs incognitac potcrunt dctcrminari cx rcgulis algcbrac, 

 confcqucntcr cft problcma propofitum dctcrminatum. Scd 

 manifelhic liunt hae otFuciac , fi perpcndatur thcnrcmu 

 hjdnftaticum , quo ccrtum cll , iaduras pondcris ciusdcin 

 maffic , ficl.is in diucrfis fluidis , cflc in rationc dcnfita- 

 tum corundem fluidorum. Sint crgo fluidorum M ct N 

 dcnfitatcs //; ct n \ atquc crit a:a — fn:f)\ b : ^ — m:n\ 

 c : y — m : n \ p : tt rr w; : « ; confcqucntcr crit a rz: 



"^ ; P = "^ ; Y = V i ^ = "^- i q"i valorcs fubfl.tuti 

 in aeqiiationc ax -^ ^y -[- y z—Vm y rcddunt primam 

 ipfinimam ax-\-bj' -hcz — Vp ; ita vt duac hac acqua- 

 tiones , non rc ipla , fcd lola fimul.itionc altcrius , app.i- 

 rcant diucrfic ; quare duae l(>lum (iiixTliint acquationes rc- 

 ales , ex quib.h adco pioblcma triuni incognitariim manct 

 indctcrminatuni. 



§.7. Supcrcft alia adhuc confidciatio , quac iubcrc 

 vidctur vt ct ilcris , iu quo corpora pondcramus , ratio 

 habcatur , fi dcnfitatcm conim , qiiantuin licct , tx:nflam 

 obtincrc vclimus. Amittuiit cnim in acrc (|Uoquc ali(]uid 

 iiii pmJcri.s corpora , quod facilc ad calculum icuocari 

 potcll. Sit igitur corporis alicuius pondus ablolutum , 



quod 



