"[T]he plural name—"The Mathematics"—would alone suffice to indicate the want of unity in the common conception of it."

"[I]t was not till the commencement of the last century that the different fundamental conceptions which constitute th…"

"The science of mathematics is now sufficiently developed, both in itself and as to its most essential application, to…"

"Every precise idea of fixed numbers is truly out of place in the phenomena of living bodies... when we attach any imp…"

"To form a just idea of the object of mathematical science... start from the indefinite and meaningless definition of …"

"Let us... rise from this rough sketch... to a veritable definition, worthy of the importance, the extent, and the dif…"

"The Object of Mathematics. Measuring Magnitudes. According to this definition... the science of mathematics—vast and …"

"The error of this definition consists in presenting as direct an object which is almost always, on the contrary, very…"

"[B]eing able to pass over the line from one end of it to the other, in order to apply the unit of measurement to its …"

"Although Mathematical Science is the most ancient and the most perfect... the general idea which we ought to form of …"