Mathematical Questions and Solutions, Band 42

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F. Hodgson, 1885
 

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Seite 131 - 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.
Seite 131 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.
Seite 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 possible influence of example, authority, education, sympathy, or habit; whether, I say, such a one would feel, upon the relation, any degree of that sentiment of disapprobation of Toranius's conduct which we feel, or not?
Seite 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.
Seite 132 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Seite 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.
Seite 137 - Having experienced, in some instance, a particular conduct to be beneficial to ourselves, or observed that it would be so, a sentiment of approbation rises up in our minds ; which sentiment afterwards accompanies the idea or mention of the same conduct, although the private advantage which first excited it no longer exist.
Seite 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.
Seite 130 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Seite 22 - A thin uniform spherical cap being supposed to attract according to the law of the inverse fifth power of the distance...

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