(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. Part V. On Perspective (published separately as _Perspectiva_). (1) The organs of vision. (2) Vision in straight lines. (3) Vision reflected and refracted. (4) De multiplicatione specierum (on the propagation of the impressions of light, heat, &c.) Part VI. On Experimental Science.] [Footnote 64: _Op. Maj._ p. 1.] [Footnote 65: _Ibid._ p. 2.] [Footnote 66: _Ibid._ p. 10.] [Footnote 67: I will give a specimen. _Opus Majus_, c. viii. p. 35: "These two kinds of philosophers, the Ionic and Italic, ramified through many sects and various successors, till they came to the doctrine of Aristotle, who corrected and changed the propositions of all his predecessors, and attempted to perfect philosophy. In the [Italic] succession, Pythagoras, Archytas Tarentinus and Timæus are most prominently mentioned. But the principal philosophers, as Socrates, Plato, and Aristotle, did not descend from this line, but were Ionics and true Greeks, of whom the first was Thales Milesius.... Socrates, according to Augustine in his 8th book, is related to have been a disciple of Archelaus. This Socrates is called the father of the great philosophers, since he was the master of Plato and Aristotle, from whom all the sects of philosophers descended.... Plato, first learning what Socrates and Greece could teach, made a laborious voyage to Egypt, to Archytas of Tarentum and Timæus, as says Jerome to Paulinus. And this Plato is, according to holy men, preferred to all philosophers, because he has written many excellent things concerning God, and morality, and a future life, which agree with the divine wisdom of God. And Aristotle was born before the death of Socrates, since he was his hearer for three years, as we read in the life of Aristotle.... This Aristotle, being made the master of Alexander the Great, sent two thousand men into all regions of the earth, to search out the nature of things, as Pliny relates in the 8th book of his _Naturalia_, and composed a thousand books, as we read in his life."] [Footnote 68: _Ibid._ p. 36.] [Footnote 69: _Autonomaticè._] [Footnote 70: _Op. Maj._ p. 46.]