Mathematical Questions with Their Solutions: From the "Educational Times"., Volumer 40-42

1884

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Side 111 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Side 112 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Side 127 - A cos. B cos. C, we have sin. A sin. B sin. C _ sin. A sin. B sin. C cos. A cos. B cos.
Side 137 - To construct a triangle, having given the base, the vertical angle, and the bisector of that angle.
Side 117 - Now, the question is, whether, if this story were related to the wild boy caught some years ago in the woods of Hanover, or to a savage without experience, and without instruction, cut off in his infancy from all intercourse with his species, and consequently under no...
Side 117 - Toranius's conduct which we feel, or not. They who maintain the existence of a moral sense ; of innate maxims ; of a natural conscience ; that the love of virtue and hatred of vice are instinctive ; or the perception of right and wrong intuitive, (all which are only different ways of expressing the same opinion,) affirm that he would. They who deny the existence of a moral sense, &c. affirm that he would not. — And, upon this, issue is joined.
Side 137 - The lenses of a common astronomical telescope, whose magnifying power is 16, and length from object-glass to eye-glass 84 inches, are arranged as a microscope to view an object placed f of an inch from the object-glass; find the magnifying power, the least distance of distinct vision being taken to be 8 inches.
Side 108 - To describe an equilateral triangle upon a given finite straight line. Let AB be the given straight line : it is required to describe an equilateral triangle upon AB.
Side 116 - X : eg Prudence has for its object the benefit of individuals ; but prudence is a virtue ; therefore, some virtue has for its object the benefit of the individual, is part of Adam Smith's reasoning (Moral Sentiments) against Hutcheson and others, who placed all virtue in benevolence.
Side 75 - C?7 +/))[• > where 4/ is the focal length of the field-glass. Find the magnifying power in this latter case. 14. The lenses of a common astronomical telescope, whose magnifying power is 16, and length from object-glass to eye-glass 8^ inches, are arranged as a microscope to view an object placed...