Mathematical Questions and Solutions, from the "Educational Times.", Volume 44

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F. Hodgson, 1886
 

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Page 111 - S sin2 c _ 1 — cos2 a — cos2 b — cos2 c + 2 cos a cos b cos c...
Page 150 - Explain the principle and construction of the Achromatic Telescope. 15. What is the least velocity with which a body must be projected from the Moon, in the direction of a line joining the centres of the Earth and Moon, so that it may reach the Earth ? 16.
Page 173 - Find the equation to the locus of a point which moves so as to be always equi-distant from the lines — — a=0.
Page 63 - If, in several couplets, the ratios are equal, THE SUM OF ALL THE ANTECEDENTS HAS THE SAME RATIO TO THE SUM OF ALL THE CONSEQUENTS, WHICH ANY ONE OF THE ANTECEDENTS HAS TO ITS CONSEQUENT.* {12: 6=2 ft • 4—2 6 : 3 = 2 Therefore the ratio of (12+10+8+6) : (6+5+4+3) = 2.
Page 63 - A man goes in for an examination in which there are four papers with a maximum of m marks for each paper ; shew that the number of ways of getting half marks on the whole is 31. Find the coefficient of œ
Page 171 - Given the base and vertical angle of a triangle, find the locus of the intersection of perpendiculars to the sides from the extremities of the base.
Page 39 - A square is divided into 16 equal squares by vertical and horizontal lines. In how many ways can 4 of these...
Page 106 - PROPOSITION 5. The locus of a point, the ratio of whose distances from two given points is constant, is a circle*.
Page 109 - Show that on a chess-board the number of squares visible is 204, and the number of rectangles (including squares) visible is 1296...

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