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abstract according affirmed Algebra analysis angles applicable argument arithmetic axioms basis branch called combinations common compared conclusion connection considered course deductive definition denominate divided division elementary elements employed entire equal equation examination example exist explain expressed facts figures four fractions Geometry give given Hence ideas implies important increase indicate induction inferred kind knowledge known language laws length logic marks mathematical mathematical science means measure merely method mind multiplied nature necessary objects observation once operations particular plane practical predicate premises present principles properties proportion proposition proved quantity ratio reasoning reference regarded relation rules scale sense separate sides signs simple solid space square straight surface syllogism symbols taken teaching term thing third tion triangle true truths unit whole
Σελίδα 307 - In the mathematics I can report no deficience, except it be that men do not sufficiently understand the excellent use of the pure mathematics, in that they do remedy and cure many defects in the wit and faculties intellectual. For if the wit be too dull, they sharpen it ; if too wandering, they fix it; if too inherent in the sense, they abstract it.
Σελίδα 335 - Rock, which stands on one side of the harbour's mouth, so nearly right ahead that we had not to alter our course above a point in order to hit the entrance of Rio. This was the first land we had seen for three months, after crossing so many seas and being set backwards and forwards by innumerable currents and foul winds.
Σελίδα 319 - Admission to its sanctuary, and to the privileges and feelings of a- votary, is only to be gained by one means — sound and sufficient knowledge of mathematics, the great instrument of all exact inquiry, without which no man can ever make such advances in this or any other of the higher departments of science as can entitle him to form an independent opinion on any subject of discussion within their range.
Σελίδα 52 - INDUCTION, then, is that operation of the mind, by which we infer that what we know to be true in a particular case or cases, will be true in all cases which resemble the former in certain assignable respects. In other words, Induction is the process by which we conclude that what is true of certain individuals of a class is true of the whole class, or that what is true at certain times will be true in similar circumstances at all times.
Σελίδα 335 - Horn. Arrived within a week's sail of Rio, he set seriously about determining, by lunar observations, the precise line of the ship's course, and its situation in it at a determinate moment, and having ascertained this within from five to ten miles, ran the rest of the way by those more ready and compendious methods, known to navigators, which can be safely employed for short trips between one known point and another, but which cannot be trusted in long voyages, where the moon is their only guide.
Σελίδα 75 - ... whatever is predicated (ie affirmed or denied) universally, of any class of things, may be predicated in like manner, (viz. affirmed or denied,) of any thing comprehended in that class.
Σελίδα 245 - AD c, have two sides, and the included angle of the one equal to two sides and the included angle of the other, each \ to each, and are equal in all their parts...
Σελίδα 29 - All definitions are of names, and of names only; but, in some definitions, it is clearly apparent, that nothing is intended except to explain the meaning of the word; while in others, besides explaining the meaning of the word, it is intended to be implied that there exists a thing, corresponding to the word.