Pauca sed matura ["few, but ripe"]

The centre and the radius of this auxiliary sphere are here quite arbitrary.

In researches in which an infinity of directions of straight lines in space is concerned, it is advantageous to represent these directions by means of those points upon a fixed sphere

The enchanting charms of this sublime science reveal themselves in all their beauty only to those who have the courage to go deeply into it.

But in our opinion truths of this kind should be drawn from notions rather than from notations.

It is not knowledge, but the act of learning, not possession but the act of getting there, which grants the greatest enjoyment.

Spherical trigonometry and certain other theorems, to which the author has added a new one of frequent application, then serve for the solution of the problems which the comparison of the various directions involved can present.