## Mensuration of lines, surfaces, and volumes1873 |

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### Common terms and phrases

12 feet 9 inches altitude arc equal area of triangle axis base Books centre chord circle whose radius circular measure circumference circumscribing common Compare cone contains cube cubic feet cylinder denote diagonal diameter difference divide draw edge ends English equal equilateral evidently Exercises expressed faces feet 6 inches figure find the area find the length Find the radius Find the volume foot frustum given half the sum height Hence hexagon inscribed Interpreting lateral surface lune magnitude mean measure multiplied parallel perimeter perpendicular plane prism PROP proposition pyramid radii ratio rectangle revolves right angle ring round sector segment shew sides similar slant height sphere square feet square inches square yards Standard subtended taking total surface trapezoid triangle triangular unit values volume whole yards

### Popular passages

Page 1 - The area of the surface generated by a straight line revolving about an axis in its plane, is equal to the projection of the line on the axis multiplied by the circumference of the circle whose radius is the perpendicular erected at the middle of the line and terminated by the axis.

Page 59 - The volume of a triangular prism is equal to the product of its base by its altitude.

Page 41 - A Cylindrical surface is a curved surface generated by a moving straight line which continually touches a given curve and in all its positions is parallel to a given fixed straight line not in the plane of the curve.

Page 42 - A conical surface is a curved surface generated by a moving straight line which continually touches a given curve, and passes through a given fixed point not in the plane of the curve. Thus, if the straight line...

Page 46 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.

Page 97 - From this it readily follows that all the three lines drawn from the angles of a triangle to the middle of the opposite sides, pass through one and the same point.

Page 46 - The axis of a circle of a sphere is the diameter of the sphere which is perpendicular to the plane of the circle. The ends of the axis are called the poles of the circle.

Page 98 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.

Page 41 - The areas of two circles are to each other as the squares of their radii, or as the squares of their diameters. S TrR2 R* If1' = ~R^ = "cT* = -D'*