234 A SHORT HISTORY OF SCIENCE 



partake of the holy communion, we must three times express our con- 

 trition, Domine non sum dignus; but who can say more of the ternary 

 number in a shorter compass, than what the prophet says, tu signaculum 

 sanctae trinitatis. There are three Furies in the infernal regions; 

 three Fates, Atropos, Lachesis, and Clotho. There are three theo- 

 logical virtues ; Fides, spes, and charitas. Tria sunt pericula mundi : 

 Equum currere; navigare, et sub tyranno vivere. There are three 

 enemies of the soul : the Devil, the world, and the flesh. There 

 are three things which are of no esteem : the strength of a porter, the 

 advice of a poor man, and the beauty of a beautiful woman. There 

 are three vows of the Minorite Friars; poverty, obedience, and 

 chastity. There are three terms in a continued proportion. There 

 are three ways in which we may commit sin : corde, ore, ope. Three 

 principal things in Paradise: glory, riches, and justice. There are 

 three things which are especially displeasing to God : an avaricious 

 man, a proud poor man, and a luxurious old man. And all things 

 in short, are founded in three ; that is, in number, in weight, and in 

 measure. 



GEOMETRY IN ART. Brunelleschi (1377-1446), the famous 

 architect of the early Renaissance, made a perspective view of the 

 Signoria in Florence in a sort of box with clouds. The famous doors 

 of the Baptistery by his contemporary Ghiberti show the develop- 

 ment of perspective in the marked contrast between the earlier 

 and the later panels. Raphael in his School of Athens includes 

 himself and Bramante in a group of mathematicians. Painters 

 were even called for a time perspectivists prospettivi. 



Leonardo da Vinci (1452-1519), one of the intellectual giants 

 of the Renaissance, eminent alike in art, science and engineer- 

 ing, gave the first correct explanation of the partial illumination 

 of the darker part of the moon's disc by reflection from the earth. 

 He calls mechanics the paradise of the mathematical sciences, 

 because through it one first gains the fruit of these sciences. He 

 denies the possibility of perpetual motion, saying "Force is the 

 cause of motion and motion the cause of force." He discusses the 

 lever, the wheel and axle, bodies falling freely or on inclined planes, 

 foreshadowing Galileo. Contrary to the Aristotelian tradition he 

 asserts that everything tends to continue in its given state, and he 



