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 66
... intersect in one point . ( Euclid , i . 4 , 8 . Cape , i . 6 , 15. ) 14. The three straight lines bisecting the angles of a triangle , intersect in one point . ( Euclid , i . 26. Cape , i . 7. ) 15. The three straight lines joining the ...
... intersect in one point . ( Euclid , i . 4 , 8 . Cape , i . 6 , 15. ) 14. The three straight lines bisecting the angles of a triangle , intersect in one point . ( Euclid , i . 26. Cape , i . 7. ) 15. The three straight lines joining the ...
Page 67
... intersect in a circle , the difference of their squares is equal to the difference of the squares of the difference of the segments . ( Euclid , ii . 8 , and iii . 35. Cape , iii . 61 , 77. ) 36. If two chords be drawn from any point of ...
... intersect in a circle , the difference of their squares is equal to the difference of the squares of the difference of the segments . ( Euclid , ii . 8 , and iii . 35. Cape , iii . 61 , 77. ) 36. If two chords be drawn from any point of ...
Page 68
... by the chord . ( Euclid , iii . 32. Cape , ii . 49. ) 52. Any two parallel lines meeting a circle cut off equal arcs . ( Euclid , iii . 21. Cape , ii . 49. ) 53. If two chords of a circle intersect at right 68 889 GEOMETRY .
... by the chord . ( Euclid , iii . 32. Cape , ii . 49. ) 52. Any two parallel lines meeting a circle cut off equal arcs . ( Euclid , iii . 21. Cape , ii . 49. ) 53. If two chords of a circle intersect at right 68 889 GEOMETRY .
Page 69
Alfred Wrigley. 53. If two chords of a circle intersect at right angles , the sum of the squares of the four segments equals the square of the diame- ter . ( Euclid , iii . 31. Cape , ii . 47. ) 54. If two chords of a circle intersect at ...
Alfred Wrigley. 53. If two chords of a circle intersect at right angles , the sum of the squares of the four segments equals the square of the diame- ter . ( Euclid , iii . 31. Cape , ii . 47. ) 54. If two chords of a circle intersect at ...
Page 70
... intersect in H ; prove that HC ( AC + EC ) = AE × EC . ( Euclid , vi . 2. Cape , iii . 66. ) 77. If a triangle ABC have a right angle C , and AD be drawn bisecting the angle A , and meeting BC in D , then shall AC2 : AD2 = BC : 2BD ...
... intersect in H ; prove that HC ( AC + EC ) = AE × EC . ( Euclid , vi . 2. Cape , iii . 66. ) 77. If a triangle ABC have a right angle C , and AD be drawn bisecting the angle A , and meeting BC in D , then shall AC2 : AD2 = BC : 2BD ...
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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...