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altitude angular points annuity annum axes axis vertical balls base bisecting body Cape cent centre of gravity centre of pressure chord circle circumference compound interest conic section cos1 cosec cube roots curve cylinder density depth determine diameter Divide drawn earth,s ellipse equal equilibrium Euclid extremity filled with fluid Find the area Find the centre find the distance Find the equation Find the height find the locus find the ratio Find the value forces frustum given point hemisphere horizontal plane hyperbola hypothenuse inches inclined plane inscribed intersection isosceles triangle latus rectum mercury middle point Multiply oscillation parabola paraboloid parallel pendulum perfectly elastic perpendicular projected pulley radii radius respectively rest right angles segment sides sin1 sphere square roots string surface tangent vertex vertical angle weight yards
Pàgina 90 - 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.
Pàgina 157 - 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°.
Pàgina 56 - 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?
Pàgina 167 - A beam, 30 feet long, balances itself on a point at one-third of its length from the thicker end ; but when a weight of 10 Ibs. is suspended from the smaller end, the prop must be moved 2 feet towards it, in order to maintain the equilibrium.
Pàgina 89 - 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.
Pàgina 123 - 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...
Pàgina 120 - 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...
Pàgina 116 - 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.
Pàgina 51 - 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.