# An Elementary Treatise on the Differential Calculus Founded on the Method of Rates of Fluxions

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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1888 edition. Excerpt: ...the altitude of the segment. Examples XV. 1. Find the sides of the largest rectangle that can be inscribed in a semicircle of radius a. The sides are a V2 and a V2. 2. Determine the maximum right cone insciibed in a given sphere. The altitude is four thirds the radius of the sphere. 3. Determine the maximum rectangle inscribed in a given segment of a parabola. The altitude of the rectangle is two thirds that of the segment. 4. Find the maximum cone of given slant height a. The radius of the base is a 4/6. 5. A boatman 3 miles out at sea wishes to reach in the shortest time possible a point on the beach 5 miles from the nearest point of the shore; he can pull at the rate of 4 miles an hour, but can walk at the rate of 5 miles an hour; find the point at which he must land. Express the whole time in terms of the distance of the required point from the nearest point of the shore. He must land one mile from the point to be reached. s 6. If a square piece of sheet-lead whose side is a have a square cut out at each corner, find the side of the latter square in order that the remainder may form a vessel of maximum capacity The side of the square is a. 7. A given weight is to be raised by means of a lever weighing n pounds per linear inch, which has its fulcrum at one end, and at a fixed distance a from the point of suspension of the weight w; find the length of the lever m order that the power required to raise the weight may be a minimum. /2aw v--8. A rectangular court is to be built so as to contain a given area c, and a wall already constructed is available for one of the sides; find its dimensions so that the least expense may be incurred. The side parallel to the wall is double each of the others. 9. Determine the maximum cylinder inscribed in...