Hints, Theoretical, Elucidatory, and Practical, for the Use of Teachers of Elementary MathematicsWhittaker & Company, 1840 - 188 páginas |
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Hints, Theoretical, Elucidatory, and Practical, for the Use of Teachers of ... Olinthus Gilbert Gregory Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD Algebra applied arithmetic axiom base circle common measure consequently construction continued fraction cosec cubic equation demon demonstration of prop diagonal diameter divide the triangle division draw equal equations Euclid Euclid's Elements example figures formulæ fraction geometry given point given ratio gonal hence incommensurable intersection investigation isosceles least common multiple less Let the student line drawn logarithmic magnitude manifestly mathematical method multiple OLINTHUS GREGORY parallel parallelogram perpendicular polygon practical principles prob PROBLEM produce propositions prospective reference pupil quadratic quadrilateral quantity rectangle remainder respectively right angle right line root rule semicircle sides Simson's sines solution square SYNTHETIC DIVISION tangents taught thing tion Trapez trapezium triangle ABC trigonometry truth unity
Pasajes populares
Página 73 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included...
Página 102 - ... D, E, in the first of these diagrams, may be respectively equal to a, b, c, d, e, in the second ; and yet, the figures are evidently not similar. Let it be shown, either by the construction of Prob. 47, p. 368, or by some other of the methods, well known to the experienced preceptor, how to effect a precise similarity, agreeably to the definition. (6.) In the demonstration of prop. 1, which is an elegant application of the principle of def. 5, book v. After the words " point A to BD," add,
Página 94 - ... a certain number of times in the preceding one. Then this last remainder will be the common measure of the proposed lines ; and, regarding it as unity, we shall easily find the values of the preceding remainders ; and, at last, those of the two proposed lines, and hence their . ratio in numbers. Suppose, for instance, we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines.
Página 75 - Any two sides of a triangle are together greater than the third side. Let ABC be a triangle ; any two sides of it together are greater than the third side, viz., the sides BA, AC, greater than the side BC ; and AB, BC, greater than AC , and BC, CA, greater than AB. Produce BA to the point D, and make AD equal to AC ; and join DC.
Página 20 - ... in a course of infallible certainty and security. Each of these hasty glances must possess the clearness of intuitive evidence, and the certainty of mature reflection; and yet must leave the reasoner's mind entirely free to turn instantly to the next point of his progress. The faculty of performing such mental processes well and readily is of great value, and is in no way fostered by the study of logic.
Página 11 - ... sur tout ce qu'ils ont appris ? Croit-on que le dégoût qui suit nécessairement un travail aussi monotone, n'arrête pas le plus souvent les progrès des jeunes gens au terme où finit leur examen , ne les porte pas quelquefois à se débarrasser...
Página 94 - Continue this process, till a remainder occur, which is contained exactly a certain number of times in the preceding one. Then this last remainder will be the common measure of the proposed lines ; and regarding it as unity, we shall easily find the values of the preceding remainders ; and at last, those of the two proposed lines, and hence their ratio in numbers. Suppose, for instance, we find GB to be contained exactly twice in FD ; BG will be the common measure of the two proposed lines.
Página 113 - ... that the moon's mean motion, and the greatest quantities of the several equations, undergo no change from gravity.
Página 23 - Four quantities are said to be proportionals when the first is the same multiple, part, or parts of the second that the third is of the fourth : that is, when - = -, the four quantities a, b, c, d, are called proportionals.
Página 20 - the chains of the logician generally consist only of two or three links. In mathematics, on the contrary, every theorem is an example of an extended progressive chain ; every proof consists of a series of assertions, of which each depends on the preceding, but of which the last inferences are no less evident, or no less easily applied, than the simplest first principles.