A collection of examples in pure and mixed mathematics, with hints and answers, by A. Wrigley and W.H. Johnstone1845 |
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Seite 72
... vertex shall be in one of the angles of the figure , and its base in one of its sides . ( Euclid , i . 37. Cape , iii . 53. Cor . 2. ) IOI . To transform any given triangle into an isosceles one of equal area . ( Euclid , i . 37. Cape ...
... vertex shall be in one of the angles of the figure , and its base in one of its sides . ( Euclid , i . 37. Cape , iii . 53. Cor . 2. ) IOI . To transform any given triangle into an isosceles one of equal area . ( Euclid , i . 37. Cape ...
Seite 73
... vertex divides the base , to construct it . ( Euclid , iii . 33. Cape , prob . 22. ) 118. Given the base , the vertical angle , and the sum of the sides of a triangle , to construct it . ( Euclid , iii . 33 , 20. Cape , prob . 22 , and ...
... vertex divides the base , to construct it . ( Euclid , iii . 33. Cape , prob . 22. ) 118. Given the base , the vertical angle , and the sum of the sides of a triangle , to construct it . ( Euclid , iii . 33 , 20. Cape , prob . 22 , and ...
Seite 77
... vertex to the base being 25 feet . 45. Find the solid content and superficies of a triangular pyra- mid , each side of whose base is 5 feet , and the perpendicular height 30 feet . 46. Find the convex surface of a cone , the diameter of ...
... vertex to the base being 25 feet . 45. Find the solid content and superficies of a triangular pyra- mid , each side of whose base is 5 feet , and the perpendicular height 30 feet . 46. Find the convex surface of a cone , the diameter of ...
Seite 101
... Given the radius vector at any point of a parabola and the angle it makes with the curve ; find the latus rectum and the posi- tion of the vertex . 45. Show that the parameter belonging to any diameter of ΠΟΙ Parabola.
... Given the radius vector at any point of a parabola and the angle it makes with the curve ; find the latus rectum and the posi- tion of the vertex . 45. Show that the parameter belonging to any diameter of ΠΟΙ Parabola.
Seite 102
... vertex of the parabola must be found . The tangent to the circle at the given point is also a tangent to the parabola at that point . The extre- mity of the given diameter of circle may conveniently be taken for the origin of ...
... vertex of the parabola must be found . The tangent to the circle at the given point is also a tangent to the parabola at that point . The extre- mity of the given diameter of circle may conveniently be taken for the origin of ...
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A Collection of Examples in Pure and Mixed Mathematics, with Hints and ... Alfred Wrigley Keine Leseprobe verfügbar - 2013 |
Häufige Begriffe und Wortgruppen
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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Seite 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.
Seite 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.
Seite 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.
Seite 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.
Seite 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...
Seite 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?
Seite 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.
Seite 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.
Seite 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.
Seite 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...