Mathematical Questions and Solutions, Τόμος 42F. Hodgson, 1885 |
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Σελίδα x
... perpendicular to the sides CA , CB ; ( 3 ) the centre of the circumscribed circle and the centre of perpendiculars are ends of a double ordinate to the transverse axis ; ( 4 ) when they lie on the branch of which C is the exterior focus ...
... perpendicular to the sides CA , CB ; ( 3 ) the centre of the circumscribed circle and the centre of perpendiculars are ends of a double ordinate to the transverse axis ; ( 4 ) when they lie on the branch of which C is the exterior focus ...
Σελίδα xii
... , Uz con- taining respectively all the terms of the first , second , and third degrees in x , y , z ; prove that u , is perpendicular to the axis of revolution and a factor of 3 ......... 71 7616. ( W. J. C. Sharp , M.A . ) xii CONTENTS .
... , Uz con- taining respectively all the terms of the first , second , and third degrees in x , y , z ; prove that u , is perpendicular to the axis of revolution and a factor of 3 ......... 71 7616. ( W. J. C. Sharp , M.A . ) xii CONTENTS .
Σελίδα xvi
... perpendicular distance from the base of the cap . - 22 7709. ( Professor Minchin , M.A. ) - A cylindrical bar of isotropic material is subject to uniform intensity of pressure over its curved surface ; prove that , if M denote the ...
... perpendicular distance from the base of the cap . - 22 7709. ( Professor Minchin , M.A. ) - A cylindrical bar of isotropic material is subject to uniform intensity of pressure over its curved surface ; prove that , if M denote the ...
Σελίδα xviii
... perpendicular to the transverse axis of two confocal conics are drawn tan- gents OP , OQ , OP ' , OQ ' to the two conics : prove that the straight lines PP ' , PQ ' , P'Q , P'Q ' each pass through one of the common foci ...
... perpendicular to the transverse axis of two confocal conics are drawn tan- gents OP , OQ , OP ' , OQ ' to the two conics : prove that the straight lines PP ' , PQ ' , P'Q , P'Q ' each pass through one of the common foci ...
Σελίδα 22
... perpendicular distance from the base of the cap . Solution by the PROPOSER . Two pairs of planes inclined at elementary angles , one pair passing through the line of connection of the particle with the vertex of the cone , and the other ...
... perpendicular distance from the base of the cap . Solution by the PROPOSER . Two pairs of planes inclined at elementary angles , one pair passing through the line of connection of the particle with the vertex of the cone , and the other ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
a₁ a²X² algebraic Axiom BIDDLE bisects Brocard Brocard circle Brocard point C₁ cards centre of similitude centroid chance chord circle circumcentre circumcircle coefficient coincide conic coordinates cos² cosec curve diagonals distance drawn ellipse equal equation fixed point focus given H₂ HANUMANTA RAU hence horizontal hyperbola inscribed intersection inverse limaçon line joining locus mid-point nine-point circle opposite P₁ parabola parallel perpendicular plane points of contact polar position probability prove R₁ radical axis radii radius respectively right angles roots sides Similarly sin² Solution by W. J. C. squares straight line symmetrical T. C. SIMMONS tangent triangle ABC trilinear coordinates values velocity vertex vertical W. J. C. SHARP whence
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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?
Σελίδα 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.
Σελίδα 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...
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 130 - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.
Σελίδα 22 - A thin uniform spherical cap being supposed to attract according to the law of the inverse fifth power of the distance...