CONTENTS. 1. To divide a line into any number of equal parts . 1 1 1 5. To find a third proportional to two given lines 6. To find a fourth proportional to three given lines. 7. To find a mean proportional to two given lines 8. To make a triangle with three given straight lines 9. To make a parallelogram equal to a triangle 10. To make a triangle equal to a given trapezium 26. Given three points in a circle, to find any number of points in the same circle. Prob. MENSURATION OF LINES. Page. 13 14 16 1. Any two sides of a triangle being given, to find the 2. Given the three sides of a triangle, to find the perpendicular from any angle to its opposite side 3. Similar figures 4. Given the chord and versed sine of an arc of a circle; to find its diameter 5. Given the chord, and the versed sine of an arc of a circle; to find the ordinate at any distance along the chord. 6. To find the deflection of the curve from the tangent to the circle, ellipse, and parabola. 7. Given the base and height of the segment of a circle, to find the length of its arc. 8. Given the radius, length of helix at the extremity of a screw-blade and length of a screw, to find its pitch. 9. Given the speed of the vessel and the number of revolutions made by the screw per minute, to find the slip of the screw per cent. Miscellaneous formulæ . MENSURATION OF SURFACES. 28 4. To find the area of a circle, ellipse, and parabola. Page. Prob. 5. To find the area of a curve by Simpson's rule 6. To find the centre of gravity of a curve by Simpson's rule.. 7. To find the area between two concentric circles Mechanical properties of materials of construction Prob. MENSURATION OF SOLIDS. 1. To find the volume of a parallelepiped. 2. To find the volume of a prismoid and wedge 3. To find the volume of a cylinder and concentric 72 76 78 4. To find the volume and surface of a sphere or globe 8. To find the volume of a segment of a sphere and 9. To find the volumes of an ellipsoid and paraboloid 10. To find the volumes and surfaces of solids of revolution by Guldinus's method 88888 83 Simpson's method of calculating the immersed volume and centre of gravity of displacement of a ship. 100 105 108 Method of computing the emerged and immersed volumes, and the point S. To find the longitudinal distance of the centre of gravity of the immersed and emerged volumes 110 112 Observations on the construction of men-of-war, being an abstract from Fincham's "Outline of Shipbuilding" 116 On the curves described by the centre of buoyancy, the metacentric curve, and the surface of the planes |