Hints, Theoretical, Elucidatory, and Practical, for the Use of Teachers of Elementary Mathematics, and of Self-taught Students: With Especial Reference to Vol. I of Hutton's Course, and Simson's Euclid, as Text-books: Also a Selection of Miscellaneous Tables, and an Appendix on the Geometrical Division of Plane Surfaces

Whittaker & Company, 1840 - 188 páginas

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Página 75 - If two triangles have two sides of the one equal to two sides of the other, each to each, and the included...
Página 96 - AB— 13 ; hence the ratio of the lines is that of 13 to 5. If the line CD were taken for unity, the line AB would be y ; if AB were taken for unity, CD would be T%.
Página 96 - 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. Put BG...
Página 20 - The language contains a constant succession of short and rapid references to what has been proved already ; and it is justly assumed that each of these brief movements helps the reasoner forwards 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.
Página 77 - 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 115 - ... of terms that had embarrassed the greatest mathematicians, and would after a great number of revolutions, entirely change the figure of the Moon's orbit. From whence this important consequence is derived, that the Moon's mean motion and the greatest quantities of the several equations, will remain unchanged, unless disturbed by the intervention of some foreign or accidental cause These tracts are inscribed to the Karl of Maccleslield, President of the Royal Society.
Página 11 - ... et par cœur , pour s'assurer de la capacité des jeunes gens qui se livrent à l'étude de ces sciences. Aussi il est arrivé souvent que les hommes les plus instruits sont •convenus de bonne foi qu'ils ne se croyaient pas assurés d'être reçus à un examen de ce -genre ,, quoiqu'il portât sur des objets fort au-dessous de leurs connaissances.
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.
Página 87 - If from a point within a circle more than two equal straight lines can be drawn to the circumference, that point is the centre of the circle.
Página 136 - Punctuality : by which is meant, that the performance of all exercises should be limited to a certain time, and then be rigorously exacted.

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