Part IV. On the Usefulness of Mathematics.

(1) The necessity of Mathematics in Human Things (published separately as the _Specula Mathematica_).

(2) The necessity of Mathematics in Divine Things.--1°. This study has occupied holy men: 2°. Geography: 3°. Chronology: 4°. Cycles; the Golden Number, &c.: 5°. Natural Phenomena, as the Rainbow: 6°. Arithmetic: 7°. Music.

(3) The necessity of Mathematics in Ecclesiastical Things.--1°. The Certification of Faith: 2°. The Correction of the Calendar.

(4) The necessity of Mathematics in the State.--1°. Of Climates: 2°. Hydrography: 3°. Geography: 4°. Astrology.