24S LECTURE XX. 



a still more useful form by the labours of Briggs and of Gunter, Descartes, 

 about the same time, was makiug considerable additions to the science of 

 algebra, and the mathematics were soon after enriched by Cavalleri's inven- 

 tion of the method of indivisibles. This method was founded on the prin- 

 ciples introduced by Archimedes, it was further improved by Wallis, and it 

 led to the still more valuable invention of the fluxional analysis. 



The laws of collision were investigated nearly at the same time in England 

 by Wren and Wallis, and in France by Iluygens. After the discoveries of 

 Archimedes and of Galileo, those of Huygens hold the third place, in the 

 order of time, among the greatest benefits that have been conferred on sci- 

 ence. His theory of cycloidal pendulums, and his doctrine of central forces 

 were the immediate foundations of Newton's improvements. 



Hooke was as great in mechanical practice, and in ingenious contrivance, 

 as Huygens was in more philosophical theory ; he was the first that applied 

 the balance spring to watches, and he improved the mode of employing pen- 

 dulums in clocks; the quadrant, the telescope, and the microscope, were ma- 

 terially indebted to him ; he had the earliest suspicions of the true nature of 

 the cause that retains the planets in their orbits ; and the multitude of his 

 inventions is far too great to be enumerated in a brief history of the progress 

 of science. 



The composition of motion, and several other mechanical and optical sub- 

 jects, are elegantly treated in the lectures published by the learned Dr. Bar- 

 row. He was professor of mathematics at Cambridge, and voluntarily re- 

 signed his chair to make way for his successor, the pride of his country, and 

 the ornament of mankind. Sir Isaac Newton was born at Woolsthorpe in 

 Lincolnshire, on Christmas day in l642, the year of Galileo's death: At the 

 age of 12 he was sent to school at Grantham, and at 18 to Cambridge. He 

 made some important improvements in algebraical analysis, and laid the 

 foundation of his admirable method of fluxions, before he was 24 years old; 

 but his modesty prevented him from immediately publishing any work on 

 these subjects. His first optical experiments were also made in the year 1666, 

 and they were communicated to the Royal Society, then in its infancy, on his 

 admission as a member, in 1672. The theory of gravitation, and the mecha- 



