## Mensuration of lines, surfaces, and volumes1873 |

### From inside the book

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**magnitude**considered the unit**magnitude**; geometry affords us the means of deducing their measures , from the length of one or more lines connected with them . The number which expresses how often a**magnitude**contains the unit , is ... Page 29

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**magnitude**. That is , in the circles ABC , DEF , C O B E D Q of different radii , AO and DQ , the angles AOB , DQE , subtended at their centres by arcs equal to their radii , are equal , whatever be the**magnitudes**of the circles . When ... Page 30

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**magnitude**, is then numerically expressed by the unit degree and its sub- divisions . Thus , for example , an angle equal to 4th of a right angle , as well as its intercepted arc , will be expressed by 12 ° 51 ′ 25 ′′ .714 ... Page 31

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**magnitude**of the angle in any circle which is subtended by an arc equal to the radius , and as an arc equal to the radius is taken for the unit arc , so this angle is taken for the unit angle , and serves for measur- ing the**magnitude**... Page 34

... " 1 11 supplement . 32. What is the

... " 1 11 supplement . 32. What is the

**magnitude**of that angle , the circular measure of whose supplement is three times the cir- cular measure of its complement ? II . MENSURATION OF SURFACES . I. - PLANE SURFACES 34 MENSURATION . 333333.### Other editions - View all

### Common terms and phrases

12 feet 20 feet 9 inches ABē ABCD altitude angle ABC angle AOB angle subtended arc equal area of ABC area of triangle axis base multiplied centre circle whose radius circular measure circular segment circumference circumscribing circle cube cylinder decagon diagonal divide edge equilateral triangle Euclid feet 6 inches feet 9 find the area find the length Find the number Find the radius find the side find the surface Find the volume foot 9 frustum generatrix half the sum Hence hypothenuse Interpreting this formula lateral surface lune magnitude number of sides parallel parallelogram plane prism PROP radii ratio rectangle rectangular parallelopiped regular hexagon regular polygon revolving round right angle right-angled triangle sector segment shew similar triangle slant height square feet square inches square yards total surface trapezoid triangle ABC triangular prism triangular pyramid unit angle vertex

### 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 40 - 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 40 - 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'*