Mathematical Questions and Solutions, Τόμος 42F. Hodgson, 1885 |
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Σελίδα vi
... drawn at random on a circular slate whose diameter is 12 inches ; find the probability that each circle intersects the other two ...... ...... 118 5200. ( S. Tebay , B.A . ) -- A small marble is thrown at random on a square table having ...
... drawn at random on a circular slate whose diameter is 12 inches ; find the probability that each circle intersects the other two ...... ...... 118 5200. ( S. Tebay , B.A . ) -- A small marble is thrown at random on a square table having ...
Σελίδα vii
... drawn at random , and then the process is repeated ; show that ( 1 ) the probability of the chosen diagonals being such as cross within the perimeter is if the two must be distinct , and if the second may be identical with the first ...
... drawn at random , and then the process is repeated ; show that ( 1 ) the probability of the chosen diagonals being such as cross within the perimeter is if the two must be distinct , and if the second may be identical with the first ...
Σελίδα ix
... drawn to any one of the points of contact , prove that ( 1 ) the product of the squares of the perpen- diculars from the focus on the sides of the polygon varies inversely as C - cos 2ma , where C is a constant which becomes unity when ...
... drawn to any one of the points of contact , prove that ( 1 ) the product of the squares of the perpen- diculars from the focus on the sides of the polygon varies inversely as C - cos 2ma , where C is a constant which becomes unity when ...
Σελίδα x
... drawn from C parallel to the asymptotes , the circle is the escribed circle opposite C ; and ( 6 ) for the remainder of that branch the circle is one of the escribed circles opposite A ' or B ' ........ 57 7415. ( Rev. T. C. Simmons ...
... drawn from C parallel to the asymptotes , the circle is the escribed circle opposite C ; and ( 6 ) for the remainder of that branch the circle is one of the escribed circles opposite A ' or B ' ........ 57 7415. ( Rev. T. C. Simmons ...
Σελίδα xi
... drawn to the ellipse a2y2 + b2x2 · ab2 from the point O ( whose co- ordinates are X , Y ) , and the tangents at P , Q , R form a triangle P'Q'R ' ; prove that the ratio k : 1 of the triangles PQR , P'Q'R ' is given by 2 - { k2 + ( k ...
... drawn to the ellipse a2y2 + b2x2 · ab2 from the point O ( whose co- ordinates are X , Y ) , and the tangents at P , Q , R form a triangle P'Q'R ' ; prove that the ratio k : 1 of the triangles PQR , P'Q'R ' is given by 2 - { k2 + ( k ...
Άλλες εκδόσεις - Προβολή όλων
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...