in 1585 at Turin, a work on geometrical analysis. About 

 the same time Simon Stevin, of Flanders, enriched arithmetic 

 by the invention of decimal fractions. Algebra was improved 

 by the genius of Jerome Cardanus, and especially by Viete of 

 France, who introduced the use of letters of the alphabet to 

 represent known quantities, thus facilitating the expression 

 of general truths. The signs plus + and minus were first 

 used in a mathematical work published in 1544, and the 

 sign equality =, appeared three years later in an English 

 algebra by Robert Recorde. The important invention of 

 logarithms by the student of astrology, John Napier, Baron 

 of Merchiston, of Scotland, was not publicly announced until 

 1618 ; while the influence of the genius of Descartes was not 

 felt until the middle of the same century. 



The foundations of the science of mechanics were laid by 

 Jerome Frascator, Jerome Cardanus and Ubaldo del Monte 

 (1577), but this mathematical science as well as physics was 

 but in its infancy at Rudolph's time. The treatise on 

 Natural Magic written by the precocious youth Giovanni 

 Baptista Porta of Naples in 1560, contained evidence that 

 the author had successfully experimented in optics, and had 

 constructed apparatus on scientific principles, capable of pro- 

 ducing such marvellous illusions as to be ascribed to magic. 

 The so-called "magic lantern" is often attributed to Porta, 

 but he had been anticipated by that wonderful master of 

 many arts, Leonardo da Vinci. Porta's treatise which went 

 through several editions, deals much with lenses and mirrors 

 of various kinds and seems to describe vaguely the telescope; 

 in fact, after Galileo had perfected the instrument known as 

 Galileo's tube, Porta claimed the invention as his own. Porta 

 was indebted to the Venetian ecclesiastic, statesman and 

 scientist Fra Paolo, whose real name was Pietro Sarpi, for 

 several items of learning, notably those concerning the pro- 



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