IMAGINAKUS CONSTRJENDIS. 195 



lationc ad aream Dti primitiui pofitiui ( Julf a. ). 

 [§. III. Vil. n. II. et III. ]. Vnde etiam mirum non ell , 

 qubd e. g. in §. XXII. {Fi^. 3. (3) V DciPlH/:— ^-V F-e. 3. 

 — ip'— y — (ip'— ^) , habeat fbimam radicis minoris, 

 contra aiitem Vati PQ0>"-f-y-:^p'4-V-(^p*-^) , for- 

 mam ndicis maioris ; item quod in §.XXII.(F/^. 5. p et>(J) ^'S. 5- 

 y Dti PIH/:— -f-y-|p'— y— (i/H-^) , radicis minoris for- 

 mam habeat , led V Dti VQurz^-^y-ip'-i-y-[lp"-hq} , 

 formam radicis maioris, Breuiter : duo eiusmodi ora ex oui> 

 {Fig. 3.)et duo Dta ex p, (ecundum congruentiam inter ^'s- 3. 

 fe comparata conflituunt proportionem Geometricam. 



E. gr SdPITK : dPQVR— dPIH^ : oVQOy? 



i , ^ , - c ; ^J^ eadcm 



C H-«5 : -H-9 — -25 : -9 > ' 



Dti (ecundum quantitatem arearum inter fe comparata , 



fecinnt proportiontm Arithmeticam. 



E.gr S^PiTK-aPQyR— DPQPr-DPIH;^? ^. ,.^ 



C -f-25— -4-9 = — 9 25 3 ' 



rcntia Terminorum vtriusque rationis td zn— 16. 



§. 25. Qiiomodo antem eiusmodi radices arearum 

 priuatinarum ex mente mca in calculo traclandae fint , in vni' 

 co cxcmpio adiefto oftendiffe (tifBcit. Nimirum,^,v§. XXIII. 

 niim II , fit conflruenda aequatio x^-zV-lp^.x+qziio , et qui- 

 dem(F/g 5- p) pro cafii .r=yDiiPIIU--:-fy-:p'-y-('/+</): ^'S- «• 

 mtx'--ip'-{lp'-\-q)-ipV[-i-{ip^-\-q)] 



=^~lp' -q -pyilp^-^q) .zrDPIHi 



■"2y-ip'.A:=r'2y-ip'[y-i/-y-(:p'H-^)] 



-_2y[_.p«_.py^_x.-(._4_,yjj] 



■=-\-\p* +py{lp"-^q) -PL.PKirPL.-P^r-aPLcI)^ 



^ q r=z -\-q ::-PQ.PK=LT.L9--LI.-LC|)=-C]LIH(:|) 



quorum fumma vtrobique eft =:: o , et praeterea calcuhis pariter ac 

 con(^ni(5tio ex affe confentit cum §. XX. num. i. 



B b a f 2j5. 



