[54]. Giordano Bruno (born 1548, burned for heresy 1600). His whole life might be expressed as a crusade on behalf of God and the Copernican universe against a degenerated orthodoxy and an Aristotelian world-idea long coagulated in death.—Tr.

[55]. F. Strunz, Gesch. d. Naturwiss. im Mittelalter (1910), p. 90.

[56]. In the “Psammites,” or “Arenarius,” Archimedes framed a numerical notation which was to be capable of expressing the number of grains of sand in a sphere of the size of our universe.—Tr.

[57]. This, for which the ground had been prepared by Eudoxus, was employed for calculating the volume of pyramids and cones: “the means whereby the Greeks were able to evade the forbidden notion of infinity” (Heiberg, Naturwiss. u. Math. i. Klass. Alter. [1912], p. 27).

[58]. Dr. Anster’s translation.—Tr.

[59]. See Vol. II, Chapter III.

[60]. Oresme was, equally, prelate, church reformer, scholar, scientist and economist—the very type of the philosopher-leader.—Tr.

[61]. Oresme in his Latitudines Formarum used ordinate and abscissa, not indeed to specify numerically, but certainly to describe, change, i.e., fundamentally, to express functions.—Tr.

[62]. Alexandria ceased to be a world-city in the second century A.D. and became a collection of houses left over from the Classical civilization which harboured a primitive population of quite different spiritual constitution. See Vol. II, pp. 122 et seq.

[63]. Born 1601, died 1665. See Ency. Brit., XI Ed., article Fermat, and references therein.—Tr.