## The Logic and Utility of Mathematics: With the Best Methods of Instruction Explained and Illustrated |

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abstract affirmed Algebra analysis Analytical Analytical Geometry angles applicable apprehended argument Aristotle arithmetic axioms basis bers branch called common compared conclusion connection copula Croton aqueduct curved deductive deductive reasoning defined definition denominate numbers denote Descriptive Geometry divided division elementary employed ence equal equation eral example explain expressed facts figures fractional units geometrical magnitudes Geometry gism Hence ical idea implies Induction inferred integer integer units Integral Calculus kind knowledge known language laws learner length Logic mathematical science means merate method metic middle term mind multiplied Natural Philosophy nature Number and Space operations Philosophy plane practical predicate premises principles proportion proposition quantity quotient ratio reasoning regarded relation rules sensible objects signification simple solid species square straight line subtraction surface syllogism symbols things tion triangle Troy Weight true truths unit of measure unity whole words yard

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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 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 1 - MATHEMATICS. The Logic and Utility of Mathematics, with the best Methods of Instruction, explained and illustrated.

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 73 - ... 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.