16 MEMORABILIA MATHEMATICA

rupted movement of thought, with distinct intuition of each
thing; just as we know that the last link of a long chain holds to
the first, although we can not take in with one glance of the eye
the intermediate links, provided that, after having run over
them in succession, we can recall them all, each as being joined to
its fellows, from the first up to the last. Thus we distinguish
intuition from deduction, inasmuch as in the latter case there is
conceived a certain progress or succession, while it is not so in
the former; . . . whence it follows that primary propositions,
derived immediately from principles, may be said to be known,
according to the way we view them, now by intuition, now by
deduction; although the principles themselves can be known
only by intuition, the remote consequences only by deduction.

DESCARTES.

Rules for the Direction of the Mind, Philosophy
of D. [Torrey] (New York, 1892), pp. 64, 65.

220. Analysis and natural philosophy owe their most impor-
tant discoveries to this fruitful means, which is called induction.
Newton was indebted to it for his theorem of the binomial and
the principle of universal gravity. LAPLACE.

A Philosophical Essay on Probabilities [Tru-
scott and Emory] (New York 1902), p. 176.

221. There is in every step of an arithmetical or algebraical
calculation a real induction, a real inference from facts to facts,
and what disguises the induction is simply its comprehensive
nature, and the consequent extreme generality of its language.

MILL, J. S.
System of Logic, Bk. 2, chap. 6, 2.

Source:



Memorabilia mathematica; or, The philomath's quotation-book - Moritz, Robert Édouard, 1868-1940