The Logic and Utility of Mathematics: With the Best Methods of Instruction Explained and Illustrated |
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Common terms and phrases
A. S. BARNES abstract affirmed Algebra analysis Analytical Geometry angles applicable apprehended argument arithmetic Avoirdupois axioms basis bers branch Calculus called common compared conclusion connection copula Croton aqueduct curved DAVIES deductive deductive reasoning defined definition denominate numbers denote DESCRIPTIVE GEOMETRY divided division elementary elements employed ence equal equation eral example explain expressed facts faculties figures fractional units gism Hence idea implies Induction inferred integer INTEGRAL CALCULUS kind knowledge known language laws length Logic mathematical science means method metic middle term mind MONTEITH'S multiplied Natural Philosophy nature objects operations plane practical predicate premises principles proportion proposition pupil quantity quotient ratio reasoning regarded relation rules sides signification simple solid species spelled square straight line subtraction surface syllogism symbols things tion triangle Troy Weight true truths unit of measure unity UNIVERSITY ALGEBRA whole words yard
Popular passages
Page 305 - 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.
Page 235 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Page 317 - 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.
Page 50 - 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.
Page 249 - The area of a rectangle is equal to the product of its base and altitude.
Page 243 - 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...
Page 60 - IN every instance in which we reason, in the strict sense of the word, ie make use of arguments, whether for the sake of refuting an adversary, or of conveying instruction, or of satisfying our own minds on any point, whatever may be the subject we are engaged on, a certain process takes place in the mind, which is one and the same in all cases, provided it be correctly conducted.
Page 252 - Similar triangles are to each other as the squares of their homologous sides.
Page 333 - Rock, which stands on one side of the harbor'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.
Page 354 - ... 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.