io6 PROGRESS OF SCIENCE. 



first mathematics, whose object, number and measure 

 arithmetic and geometry treat with sovereign truth of the 

 discontinuous and continuous quantity. 



" No human investigation can ba called true science if it 

 does not pass through mathematical demonstrations. 



" Those who are infatuated by practice without science 

 are like the navigator who sails a ship without helm and 

 compass ; he never knows with certainty whither he goes. 

 Practice must always be built upon theory. Study science 

 first, then follow the practice which is born from science. 

 Hence the treatise of the mechanical sciences must precede 

 the treatise of useful inventions. 



" We call science a sequence of reasonings (quale discorso 

 mentale) which takes for its starting-point the last principles out- 

 side which in nature nothing can be found but is a part of that 

 science." That is experience as a point of departure, and the 

 mathematical form as a point of conclusion ; such is his con- 

 ception of science a conception endorsed by modern science. 



Leonardo respects the ancients,andwithdiscrimination even 

 protects them against the commentators who distort them : 



" Some commentators," he says, " blame ancient inventors 

 who gave birth to grammar and to the sciences, and stand 

 forth like errant-knights (e fansi cavalier?) against dead 

 inventors ; and because they are incapable to become inventors 

 themselves, they are through sloth and the convenience of 

 books, carelessly occupied to cavil at their masters by false 

 arguments." . . . And then we find him consulting the 

 ancients with care and admiring them : with true scientific 

 sense he admired Archimedes beyond any. And respecting 

 the ancients he does not fail to assail the Schoolmen together 

 with authority : 



" Many will think they can reasonably blame me, alleging 

 that my proofs go counter to the authority of some great 

 men held in high reverence through their uncontrolled 

 judgments (inespertf) t not considering that my ideas are born 

 from pure and simple experiment which is my true mistress. 

 If I do not, like them, quote authors, I shall invoke a thing 

 much higher and more worthy viz. experiment which is 

 their master's mistress. 



