The Mathematical Questions Proposed in the Ladies' Diary: And Their Original Answers, Together with Some New Solutions, from Its Commencement in the Year 1704 to 1816, المجلد 3

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الصفحة 58 - The length, tension, and weight of a musical string being given, it is required to find how many vibrations it will make iu a given time, when a small given weight is fastened to its middle and vibrates with it.
الصفحة 113 - In a triangle, having given the ratio of the two sides, together with both the segments of the base, made by a perpendicular from the vertical angle, to determine the sides of the triangle.
الصفحة 261 - If a heavy sphere, whose diameter is 4 inches, be let fall into a conical glass, full of water, whose diameter is 5, and altitude 6 inches ; it is required to determine how much water will run over ? AHS.
الصفحة 174 - The resistance of a cylinder moving in any fluid, is equal to the weight of a cylinder of that fluid, of the same base, and its length equal to the height a body falls in vacua, to acquire its velocity.
الصفحة 257 - If three quantities be proportional, the product of the two extremes is equal to the square of the mean ; for, if a : b '.; b : c, then, by theorem 1, ac=b3.
الصفحة 345 - II, (Art. 144.) the sum of the sides is to their difference ; as the tangent of half the sum of the opposite angles, to the tangent of half their difference. Therefore, R : tan (ACH— 45°) : : tan £(ACB+B) : tan i(ACB-B) Ex.
الصفحة 156 - ... side subtending the obtuse angle is greater than the squares on the sides containing the obtuse angle, by twice the rectangle contained by the side on which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. The square on the side of an equilateral triangle is equal to three times the square on the radius of a circle which passes through its angular points. 2. The opposite angles of any quadrilateral...
الصفحة 294 - ... in passing out of water into air, the sine of the angle of incidence is to that of refraction, as 3 to 4, and to that of deviation, as 3 to 1. Hence a ray of light cannot pass out of water into air at a greater angle of incidence than 48° 36', the sine of which is to radius as 3 to 4. Out of glass into air the angle must not exceed 40° 11', because the sine of 40° 11...
الصفحة 277 - It is required to find three numbers in arithmetical progression, such, that the sum of every two of them may be a square.
الصفحة 391 - Now the distance of the centre of oscillation from the point of suspension...

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