A collection of examples in pure and mixed mathematics, with hints and answers, by A. Wrigley and W.H. Johnstone. By A. Wrigley1857 |
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عبارات ومصطلحات مألوفة
altitude angular points axes axis vertical balls base bisecting body cent centre of gravity chord circumference conic section cos² cosec curve cylinder density depth determine diameter Divide drawn ellipse equal equilibrium extremity feet filled with fluid Find the area Find the centre find the distance Find the equation find the locus find the ratio Find the value forces frustum given point hemisphere horizontal plane hyperbola hypothenuse inches inclined plane intersection isosceles triangle latus rectum mercury middle point Newton's Method oscillation parabola paraboloid parallel pendulum perfectly elastic perpendicular projected prove pulley radii radius respectively rest right angles right-angled triangle roots segment sides sin² sphere square string surface tangent triangle ABC vertex vertical angle weight yards
مقاطع مشهورة
الصفحة 80 - 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.
الصفحة 108 - 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.
الصفحة 122 - To express the area of a triangle in terms of the coordinates of its angular points.
الصفحة 115 - The product of all the straight lines that can be drawn from one of the angles of a regular polygon of n sides inscribed in a circle whose radius is a to all the other angular points is па"'1. 8. If £>,, рг, •••i>2„_, , p...
الصفحة 47 - 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?
الصفحة 151 - V up a smooth plane inclined at an angle of 30° to the horizon, and 2 V the other with a velocity -^- at an elevation of 60°.
الصفحة 147 - Q, support each other on two planes, inclined to the horizon at angles a and /3 respectively, by means of a string passing over the common vertex of the planes. Find the ratio of P to Q, and the tension of the string.
الصفحة 54 - M=J_. ! + !=!. xyx + yy? f a2 2. A man wishes to make up as many different parties as he can out of 20 friends, each party consisting of the same number. How many should he invite at a time, and how many parties will there be ? 3. If on an average 2 ships out of 5 return safe to port, what is the chance that out of 5 ships expected at least two will return ? 4. A man wishes to build a wall 31 feet long, and has stones of 4 different lengths: viz., 2.2 feet, 2.5 feet, 3 feet, 4.1 feet.
الصفحة 52 - The number of balls in a triangular pile is to the number in a square pile having the same number of balls in the side of the base, as 6 to 11 ; required the number in each pile.
الصفحة 49 - D, whose shares were in geometrical progression ; and the difference between the greatest and' least, was to the difference between the two means, as 37 to 12.