A collection of examples in pure and mixed mathematics, with hints and answers, by A. Wrigley and W.H. Johnstone1845 |
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Side 65
... angle of a triangle , are at right angles to each other . ( Euclid , i . 13 . Cape , i . 2. ) 6. From two given points , to draw two straight lines to meet in a given straight line , and to make equal angles with it . ( Euclid , i . 12 ...
... angle of a triangle , are at right angles to each other . ( Euclid , i . 13 . Cape , i . 2. ) 6. From two given points , to draw two straight lines to meet in a given straight line , and to make equal angles with it . ( Euclid , i . 12 ...
Side 66
... right - angled triangle , the line drawn from the right angle to the middle point of the hypothenuse is equal to half the hypothenuse . ( Euclid , i . 26 , 34. Cape , i . 7 , 26. ) 17. In a right - angled triangle , the angle contained ...
... right - angled triangle , the line drawn from the right angle to the middle point of the hypothenuse is equal to half the hypothenuse . ( Euclid , i . 26 , 34. Cape , i . 7 , 26. ) 17. In a right - angled triangle , the angle contained ...
Side 67
Alfred Wrigley. formed by these lines are together equal to twice as many right angles wanting eight as the polygon has sides . ( Euclid , i . 32. Cor . 2 . Cape , i . 26. ) 29. If from any angle of a triangle , a straight line be drawn ...
Alfred Wrigley. formed by these lines are together equal to twice as many right angles wanting eight as the polygon has sides . ( Euclid , i . 32. Cor . 2 . Cape , i . 26. ) 29. If from any angle of a triangle , a straight line be drawn ...
Side 68
... angles equal to it , the straight lines being produced , shall touch the ... right angle . ( Euclid , iii . 31. Cape , ii . 47. ) 48. To find a point ... right 68 889 GEOMETRY .
... angles equal to it , the straight lines being produced , shall touch the ... right angle . ( Euclid , iii . 31. Cape , ii . 47. ) 48. To find a point ... right 68 889 GEOMETRY .
Side 69
... right angles , and thus cut off four arcs , the sum of any two opposite arcs equals the sum of the other two ... angle contained by these lines is double the angle con- tained by the chord joining the points of contact , and the diameter ...
... right angles , and thus cut off four arcs , the sum of any two opposite arcs equals the sum of the other two ... angle contained by these lines is double the angle con- tained by the chord joining the points of contact , and the diameter ...
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A Collection of Examples in Pure and Mixed Mathematics, with Hints and ... Alfred Wrigley Ingen forhåndsvisning - 2013 |
Almindelige termer og sætninger
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
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Side 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.
Side 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.
Side 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.
Side 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.
Side 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...
Side 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?
Side 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.
Side 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.
Side 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.
Side 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...