5. To p. 51. _Mordentius._--Fabrizio Mordente of Salerno was a mathematician of the sixteenth century, of whom only two works are known to have existed,--one published in 1597, the other written in conjunction with his brother Gaspar in 1591. He was the inventor of an eight-point compasses of which Bruno writes in the second of the Mordentius dialogues, and on which he bestows apparently extravagant praise. The peculiarity of the invention, as far as one can discover, consisted in the introduction of four "runners," two on either limb of the compasses, and secured by screws; but there seems to have been no gradation of the compasses, and it is difficult to perceive any great value in the novelty, without that essential addition. The first of the two dialogues suggests a possible origin for some of Bruno's ideas on atomic geometry, as we find, attributed to Mordentius, two ideas that were applied to some purpose in Bruno's own mathematical works. They are (1) that of the measurement of inappreciable subdivisions of continuous quantities by integration, and (2) that of the impossibility of infinite division, the continuous being composed of discrete minima, beyond which no division can go, and the _minima_ (like the _maxima_) being relative, differing in different subjects, so that, for example, what in _astronomy_ is a minimal quantity may in _geodesy_ be greater than the diameter of the earth. INDEX Absolute, first principle or, 166 Agrippa of Nettesheim, Cornelius, 148, 149; _De occulta philosophia_, 131, 149; _De Vanitate Scientiarum_, 149, 257 Alasco, Prince, of Poland, 23 Algerio, Pomponio, 4 Alsted, John Henry, _Artificium perorandi_, 114 Anaxagoras, 126 Animism, 305; universal, 147 _Antidicsonus_, 36, 324 Aquinas, St. Thomas, 9, 80, 137 Areopagus, literary society, 27 Aretino, Pietro, _Cortegiana_ of, 19 Arian heresy, the, 357 Aristotle, _De Anima_, 16, 158, 159; criticism of, 50, 123; _Organon_, 53, 55; _Topics_, 55; _Metaphysics_, 113, 125; _Rhetoric_, 114, 138; _Physics_, 115, 116, 122, 125, 236; _De generatione et corruptione_, 116; _Meteorologica_, 116; Bruno's acquaintance with, 121-23; rejection of mathematical method, 123; treatment of predecessors, 124; _Logic_, 138; theory of limitation of space, 183; on finitude of world, 185, 186; on plurality of worlds, 197 Asinity, 257 Aspiration, 291 Atom, the, 236; knowledge implies the, 227; spherical, 240; and materialism, 249 Atomism, belief of Bruno and Cusanus in, 147; a metaphysical doctrine, 227, 246; mathematical, 245; physical, 247; critical, 247; and mathematics, 331 Avarice, 272 Avenarius, 337 Averroes, 136, 305 Avicebron or Avencebrol, _Fons Vitae_, 135