420 A SHORT HISTORY OF SCIENCE 



recited word for word. At Rome in the Convent of Minerva, 22nd 

 June, 1633. 



I, Galileo Galilei, have abjured as above with my own hand. 



From ROUTLEDGE. History of Science. See also K. VON GEBLER. 

 Galileo Galilei and the Roman Curia. London, 1879. 



F. PREFACE TO THE 

 PHILOSOPHISE NATURALIS PRINCIPIA MAT HEMATIC A (1686) 



BY ISAAC NEWTON 



Since the ancients (as we are told by Pappus) made great account 

 of the science of mechanics in the investigation of natural things ; 

 and the moderns, laying aside substantial forms and occult qualities, 

 have endeavored to subject the phenomena of nature to the laws of 

 mathematics, I have in this treatise cultivated mathematics so far as 

 it regards philosophy. The ancients considered mechanics in a two- 

 fold respect; as rational, which proceeds accurately by demonstra- 

 tion, and practical. To practical mechanics all the manual arts be- 

 long, from which mechanics took its name. But as artificers do not 

 work with perfect accuracy, it comes to pass that mechanics is so 

 distinguished from geometry, that what is perfectly accurate is called 

 geometrical ; what is less so is called mechanical. But the errors 

 are not in the art but in the artificers. He that works with less ac- 

 curacy is an imperfect mechanic : and if any could work with perfect 

 accuracy, he would be the most perfect mechanic of all ; for the 

 description of right lines and circles, upon which geometry is founded, 

 belongs to mechanics. Geometry does not teach us to draw these 

 lines, but requires them to be drawn ; for it requires that the learner 

 should first be taught to describe these accurately, before he enters 

 upon geometry ; then it shows how by these operations problems may 

 be solved. To describe right lines and circles are problems, but not 

 geometrical problems. The solution of these problems is required 

 from mechanics ; and by geometry the use of them, when so solved, 

 is shown ; and it is the glory of geometry that from those few principles, 

 fetched from without, it is able to produce so many things. There- 

 fore geometry is founded in mechanical practice and is nothing but 

 that part of universal mechanics which accurately proposes and 

 demonstrates the art of measuring. But since the manual arts are 



