aia MED1T4TI0NES DE QyANTmTIBVS 



fcd id (;iltem oftendiiiit , fi h:ibc.intur aeqiuuiones com- 

 plec:ic defiiiientes , pro fingulis i(Us qu.itiior diuerfis cubis 

 diucr(ie , e.iedennque ita tiansformciuiir , vt Terminu^ (c- 

 cundus , acque vti in acqu.itionc gencrali rcfpondente , defi- 

 ciac •, quacunque libet trium radicum pro pnnia a^fumta , 

 tres aequitioni> ;ran-t(.)rm.itae radiccs cfle intcr fc , vt - i ; 

 ( ^tidpL-n: . (=t^-» (§. XXXVl) ; atque fic , vn.i radi- 

 ce cogiiita , rcliqius , opc huiu> relationis , cxpeditc for- 

 mari po^Te. E(\ autcm — ^— ' rr i -f- V — i .V ^. Vnde 

 cum , pofito finu toto ~-f-i , ct fcmiperipheriu — tt , 

 fit cof 7r~— I — cof 3 Trrr cof 5 tt , aut in gcnere :zz 

 co( (i/:-!- I )tt , littera k quemlibet numcnim nitigrum 

 denotante , ct practerca fit co(. 5 tt — H- J , fin 5 tt — ^ J ; 

 perlpicuum clt , in aequatione cubica pui^ .v' * * -1- tf* — o , 

 tres eius radices hanc inter (e rclationcm habcre , vt — i ^ 

 -i-j+ V-i. Vl i 4-j-y-i . Vi , h. e. vtcoi. (2^4- O^^i 

 cof J-rr-f- V— I . fm.^Tr; cof ^Tr- V — i . fiu ^tt ; et 

 duarum polam.uum fidlum e^Tc vt (cof Jtt) * -f (fin. \ tt)* 

 r:= I =z(— I )*— [cof (2/k-h I )7r J* , (cu vt quidratum 

 radicis prim.ie ; ficflum dtniquc ex omnibtis tribus radici- 

 bn.s , - 2 . (^*^-^)(-^^-')i=-i , e(rc vt cof [2k+ 1 )7r. 

 [cof (2jk-i- I )7r]*ci [c<>f.(2/k-H I )7r]* , (cu vt cubum 

 cubo finiis torius oppoficum (§ XXXXl) , cuius bafjs c(l 

 quidratum , prioris bafi quadratae oppofitum Vt adco 

 hic Ciibus vidcatur mcntiri (()rmam Cubi a . ? t ex 

 §. XXXXI. 



§• 47- Qiii'1 autcm cx acquatione cubica complcta 

 Tcrminus (ccu'idus tollitur , lingulas cias tns radiccs x , 

 h. c. omncb tres Cubi dimcnfioncs , caUcm quaniitato 



data , 



