86 ŒU\UES ni: FEUMAT. - 1"^ PARTIE. 



quatuor puncla X, N. D. R {fig- 7O), quai per recfas XH, RD, DN, 

 NX coiijuugantur, et ncutra oppositarum sit alteri aH|uidistans. 



Ponatur jani l'actum esse, et descriptam parabolen XANDBR [uopo- 

 sito satisfaciontem. Concurrant productse XN, RD, in puiicto Y ol. 

 Iiir;ii'i:un divisis X\, RD in punctis M et C, ducantur ad ipsas dia- 

 nietii MA, ('.B, oceurrentes parabol;v in punctis A et B, a quibus recta? 

 lAS, SBipsisXV, YR ducantur teqiiidistantes et concurrant in puncto S. 

 Jnncta AB bifariani (Iivi(hilur in P et jungatur SP. 



Fig. 76. 



His ita constructis, patet, quuni pcr verticem diametri MA ducatur 

 lAS .Tquidistans applicalse XN, rectani lAS tangere parabolen in A; 

 prol)abitur similiter rectam SB tangere camdem parabolen in B : ergo, 

 per 17, III ApoUonii crit 



ut rcclangulutn \VN ad reclaiigulum RVI), 

 ita qiiadraluin AS ad (|ua(lralum SB. 



Daturaulem ratio rectanguli XYN ad rectanguluin RVD, quuin denlur 

 quatuor puncta X, N, D, R : ergo datur ratio quadrati AS ad qua- 

 dratum SB, ideoque rectae AS ad rectam SB. Datur autem angulus ASB, 

 quia propter parallelas aujuatur angulo XYR date : ergo in trian- 

 gulo ASB datur angulus ad verticem S et ratio laterum AS, SB, ideoque 



