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Mathematical Questions with Their Solutions, from the Educational Times
D. Biddle,W. J. C. Miller
Ingen forhåndsvisning tilgjengelig - 2015
angles appear axes axis becomes cards centre chance chord circle coincide Coll College common conic constant coordinates curve described determine diagonals direction distance draw drawn edges ellipse equal equation expression figure fixed focus follows force four function given gives hence horizontal identical intersection inverse length less limit line joining locus Mathematics mean meet mid-point motion opposite origin parallel passes perpendicular placed plane polar position possible probability produced Professor PROPOSER prove question radius random ratio referred represented respectively result right angles roots sides similar Similarly Solution space squares straight line successive suppose symmetrical taken tangents things throws triangle vertical whence whole
Side 130 - LET it be granted that a straight line may be drawn from any one point to any other point. 2. That a terminated straight line may be produced to any length in a straight line.
Side 137 - 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 137 - 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 - Upon the whole, it seems to me, either that there exist no such instincts as compose what is called the moral sense, or that they are not now to be distinguished from prejudices and habits...
Side 128 - 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 136 - every one who possesses prudence ;" and you will have the celebrated argument of Aristotle, Eth. sixth book, to prove that the virtues are inseparable ; viz. He who possesses prudence, possesses all virtue ; He who possesses one virtue, must possess prudence; therefore He who possesses one, possesses all.
Side 130 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Side 136 - 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.