THE AUTHOR’S

PREFACE

TO THE

R E A D E R

Since the ancients (according to Pappus Pappus of Alexandria was a Greek mathematician of the 4th century AD whose Collection is a major source for ancient geometry.) held mechanics in the highest esteem for the investigation of natural things; and since more recent thinkers, having set aside "substantial forms" and "hidden qualities" Newton is rejecting the Aristotelian tradition, which explained the world through internal "essences" rather than external, measurable forces., have attempted to bring the phenomena of nature under mathematical laws: it seemed appropriate in this treatise to cultivate mathematics original: "mathesin." insofar as it relates to philosophy original: "philosophiam." In the 17th century, "natural philosophy" was the term for what we now call science..

The ancients established a twofold mechanics: rational mechanics, which proceeds accurately through demonstrations, and practical mechanics. To practical mechanics belong all the manual arts, from which the name "mechanics" was originally borrowed. However, since craftsmen usually work with little accuracy, it has come to pass that all mechanics is distinguished from geometry in such a way that whatever is accurate is referred to geometry, and whatever is less accurate to mechanics.

Yet the errors are not in the art, but in the craftsmen. He who works less accurately is a more imperfect mechanic, and if anyone could work with perfect accuracy, he would be the most perfect mechanic of all. For the descriptions of straight lines and circles, upon which geometry is founded, belong to mechanics. Geometry does not teach how to draw these lines, but requires it original: "postulat." In mathematics, a postulate is a starting assumption or required action.. It requires that the student original: "tyro." A beginner or apprentice. learn to describe these accurately before he reaches the threshold of geometry; then, geometry teaches how problems may be solved through these operations. To draw straight lines and circles are indeed "problems," but they are not geometric problems. The solution to these is required from mechanics; the use of those solutions is taught in geometry.

And geometry glories in the fact that, from so few principles borrowed from elsewhere, it can accomplish so many things. Geometry is therefore founded upon mechanical practice, and is nothing other than that part of universal mechanics which accurately proposes and demonstrates the art of measuring. However, since the manual arts are chiefly concerned with the moving of bodies, it follows that geometry relates to magnitude, and mechanics [to motion]... The text ends mid-word at "mechani-", which will continue as "mechanica" on the next page.