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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 definition denominate divided division elementary employed entire equal equation example existence explain expressed facts feet figures four fractions Geometry give given Hence idea important increase indicated induction inferred kind knowledge known language laws length Logic marks mathematical mathematical science means measure merely method mind multiplied nature necessary notion numbers objects observed once operations particular practical predicate premises present principles properties proportion proposition proved quantities question ratio reasoning reference regarded relation rules scale sense separately side signs simple solid space square stand surface syllogism symbols taken teaching term thing third tion true truths unit unity weight whole yards
Σελίδα 233 - 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.
Σελίδα 303 - 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 315 - 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 48 - 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 283 - The part of the equation which is on the left of the sign of equality is called the first member ; the part on the right of the sign of equality, the second member.
Σελίδα 58 - 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.
Σελίδα 65 - the trees flourish, because the ground is rich," or " the ground is rich, and therefore the trees flourish," I am using the very same conjunctions to denote the connection of cause and effect ; for in this case, the luxuriance of the trees, being evident to the eye, would hardly need to be proved, but might need to be accounted for.
Σελίδα 247 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 241 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.