quatuor puneta X, N, D, R (fig. 76), que per rectas XR, RD, DN, NX conjungantur, et neutra oppositarum sit alteri æquidistans.
Ponatur jam factum esse, et descriptam parabolen XANDBR proposito satisfacientem. Concurrant productS XN, RD, in puncto V et, bifariam divisis XN, RD in punctis M et C, ducantur ad ipsas diametri MA, CB, occurrentes parabolk in punctis A et B, a quibus recta IAS, SB ipsis XV, VR ducantur equidistantes et concurrant in puncto S. Juncta AB bifariam dividatur in P et jungatur SP.
His ita constructis, patet, quum per verticem diametri MA ducatur IAS æquidistans applicatUe XN, rectam IAS tangere parabolen in A; probabitur similiter rectam SB tangere eamdem parabolen in B: ergo, per 17, III Apollonii erit
ita quadratum AS ad quadratum SB.
Datur autem ratio rectanguli XVN ad rectangulum RVD, quurn dentur quatuor puncta X, N, D, R: ergo datur ratio quadrati AS ad quadratum SB, ideoque rectse AS ad rectam SB. Datur autem angulus ASB, quia propter parallelas æquatur angulo XVR dato: ergo in triangulo ASB datur angulus ad verticem S et ratio laterum AS, SB, ideoque
