A collection of examples in pure and mixed mathematics, with hints and answers, by A. Wrigley and W.H. Johnstone1845 |
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Page 69
... straight line , and shall also touch another straight line inclined at a given angle to the former . ( Euclid , iii . 16. Cape , ii . 38. ) 67. If an equilateral triangle be inscribed in a circle GEOMETRICAL DEDUCTIONS . 69.
... straight line , and shall also touch another straight line inclined at a given angle to the former . ( Euclid , iii . 16. Cape , ii . 38. ) 67. If an equilateral triangle be inscribed in a circle GEOMETRICAL DEDUCTIONS . 69.
Page 99
... inclined to one another at 135 ° or 45 ° . 26. The equation 2y2-3xy - 2x2 - y + 2x = 0 represents two straight lines at right angles to one another . 27. Find the polar equation to a straight line ; and trace the cos ( 0 + % ) . line ...
... inclined to one another at 135 ° or 45 ° . 26. The equation 2y2-3xy - 2x2 - y + 2x = 0 represents two straight lines at right angles to one another . 27. Find the polar equation to a straight line ; and trace the cos ( 0 + % ) . line ...
Page 100
... inclination of the axes when the lines repre- sented by the equation y2x2 = 0 are perpendicular to one another ? 35. Find the equation to a line touching a given circle , and parallel to a given straight line . 36. In the figure to ...
... inclination of the axes when the lines repre- sented by the equation y2x2 = 0 are perpendicular to one another ? 35. Find the equation to a line touching a given circle , and parallel to a given straight line . 36. In the figure to ...
Page 102
... inclined to it . The polar equation should be assumed in this case . 46. Describe a parabola which shall touch a given circle at a given point , and have its axis coincident with a given diameter of the circle . In this case the latus ...
... inclined to it . The polar equation should be assumed in this case . 46. Describe a parabola which shall touch a given circle at a given point , and have its axis coincident with a given diameter of the circle . In this case the latus ...
Page 103
... inclined to the axis of x that the sum of the co- tangents of the angles which they make with that axis is constant ; prove that the locus of their intersections is a straight line parallel to the axis . 59. If several parabolas have ...
... inclined to the axis of x that the sum of the co- tangents of the angles which they make with that axis is constant ; prove that the locus of their intersections is a straight line parallel to the axis . 59. If several parabolas have ...
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A Collection of Examples in Pure and Mixed Mathematics, with Hints and ... Alfred Wrigley No preview available - 2013 |
Common terms and phrases
angle of elevation arithmetic means arithmetic series arithmetical progression axes axis base bisecting Cape cent centre of gravity chord circumference coefficient cone conic section cos² curve described diameter direction Divide ellipse equal equilibrium Euclid expansion extremity find the angle Find the area Find the distance Find the equation find the inclination find the locus Find the ratio Find the value Formulæ fraction frustum geometrical progression given circle given point given straight line harmonic means horizontal plane hyperbola hypothenuse inches inclined plane infinity inscribed intersect latus rectum length lines be drawn middle point miles Multiply number of balls number of combinations parabola parallel pendulum perpendicular prob prove pulley radii radius respectively rest right angles right-angled triangle segments sides sin² Sum the series take moments tangent uniform beam vertex vertical angle weight yards
Popular passages
Page 69 - AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part.
Page 44 - A vintner draws a certain quantity of wine out of a full vessel that holds 256 gallons ; and then filling the vessel with water, draws off the same quantity of liquor as before, and so on for four draughts, when there were only 81 gallons of pure wine left.
Page 45 - A detachment of soldiers from a regiment being ordered to march on a particular service, each company furnished 4 times as many men as there were companies in the regiment ; but these being found insufficient, each company furnished three more men, when their number was found to be increased in the proportion of 17 to 16.
Page 67 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle,. shall be equal to the square of the line which touches it.
Page 93 - Wanting to know my distance from an inaccessible object 0, on the other side of a river; and having no instrument for taking angles, but only a chain or cord for measuring distances; from each of two stations, A and B, which were taken at 500 yards asunder, I measured in a direct line from the object 0 100 yards, viz. AC and BD each equal to...
Page 48 - A and B set out to meet each other. A went 3 miles the first day, 5 the second, 7 the third, and so on. B went 4 miles the first day, 6 the second, 8 the third, and so on. In how many days did they meet?
Page 89 - The area of a regular polygon inscribed in a circle is a geometric mean between the areas of an inscribed and a circumscribed regular polygon of half the number of sides.
Page 49 - Required the number. 9. A person employed 3 workmen, whose daily wages were in arithmetical progression. The number of days they worked was equal to the number of shillings that the second received per day. The whole amount of their wages was 7 guineas, and the best workman received 28 shillings more than the worst.
Page 44 - A detachment of an army was marching in regular column, with 5 men more in depth than in front ; but upon the enemy coming in sight, the front was increased by 845 men ; and by this movement the detachment was drawn up in 5 lines. Required the number of men.
Page 98 - If from one of the angles of a rectangle a perpendicular be drawn to its diagonal, and from, the point of their intersection lines be drawn perpendicular to the sides which contain the opposite angle...