Great Throughts Treasury

"Primary causes are unknown to us, but are subject to simple and constant laws, which may be discovered by observation, the study of them being the object of natural philosophy."

"The deep study of nature is the most fruitful source of mathematical discoveries. By offering to research a definite end, this study has the advantage of excluding vague questions and useless calculations; besides it is a sure means of forming analysis itself and of discovering the elements which it most concerns us to know, and which natural science ought always to conserve. "

"The integrals which we have obtained are not only general expressions which satisfy the differential equation, they represent in the most distinct manner the natural effect which is the object of the phenomenon... when this condition is fulfilled, the integral is, properly speaking, the equation of the phenomenon; it expresses clearly the character and progress of it, in the same manner as the finite equation of a line or curved surface makes known all the properties of those forms. "

"Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them."

"The profound study of nature is the most fertile source of mathematical discovery."