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abstract according addition affirmed Algebra analysis angles applicable argument arithmetic axioms basis branch called combinations common compared conclusion connection considered contains course deductive defined definition denominate divided division elementary elements employed entire equal equation examined example exist explain expressed facts figures four fractions Geometry give given Hence idea illustrated implies important increase indicated 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 practical predicate premises present principles properties proportion proposition proved quantities ratio reasoning reference regarded relation rules scale separate sides simple solid space square surface syllogism symbols taken teaching term tests thing third tion triangle true truths unit whole
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 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.