[41.] Theor. XII. Prop. XV.

[42.] Theor. XIII. Prop. XVI.

[43.] Theorema XIV. Propos. XVII.

[44.] Theor. XV. Propos. XVIII.

[45.] Theor. XVI. Propos. XIX.

[46.] Problema IV. Propos. XX.

[47.] Christiani Hugenii C. F. ILLVSTRIVM QVORVNDAM PROBLEMATVM CONSTRVCTIONES. Probl. I. Datam ſphæram plano ſecare, ut portiones inter ſe rationem habeant datam.

[48.] LEMMA.

[49.] Probl. II. Cubum invenire dati cubi duplum.

[50.] Probl. III. Datis duabus rectis duas medias propor-tionales invenire.

[51.] ALITER.

[52.] ALITER.

[53.] Probl. IV.

[54.] Probl. V.

[55.] Probl. VI.

[56.] Probl. VII.

[57.] Utrumque præcedentium Aliter.

[58.] Probl. VIII. In Conchoide linea invenire confinia flexus contrarii.

[59.] FINIS.

[60.] DE CIRCULI ET HYPERBOLÆ QUADRATURA CONTROVERSIA.

[61.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA AUTHORE JACOBO GREGORIO. LECTORI GEOMETRÆ SALUTEM.

[62.] DEFINITIONES.

[63.] PETITIONES.

[64.] VERA CIRCULI ET HYPERBOLÆ QUADRATURA.

[65.] PROP. I. THEOREMA. Dico trapezium B A P I eſſe medium propor-tionale inter trapezium B A P F, & triangulum B A P.

[66.] PROP. II. THEOREMA. Dico trapezia A B F P, A B I P ſimul, eſſe ad du- plum trapezii A B I P, ſicut trapezium A B F P ad polygonum A B D L P.

[67.] PROP. III. THEOREMA. Dico triangulum B A P, & trapezium A B I P ſimul, eſſe ad trapezium A B I P, ut duplum trapezii A B I P ad polygonum A B D L P.

[68.] PROP. IV. THEOREMA. Dico polygonum A B E I O P eſſe medium pro- portionale inter polygonum A B D L P & trapezium A B I P.

[69.] PROP. V. THEOREMA.

[70.] SCHOLIUM.