## Mensuration of lines, surfaces, and volumes1873 |

### From inside the book

Results 1-5 of 51

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**base**and perpendicular height ......... .. III . To find the area of a triangle , having given its**base**and perpendicular height .... IV . To find the area of a triangle , when the three sides are given ... 165 35 36 36 37 V. To find ... Page 7

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**base**by the height .... IV . To find the surface of a solid ring .................. . V. The lateral surface of a regular pyramid is equal to the product of the perimeter of the**base**by one - half the slant height .... VI . The lateral ... Page 8

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**base**........ IX . Volume of frustum of pyramid .. X. Volume of cone .... XI . Volume of frustum of cone . XII . Volume of wedge ...... $ 4 87 825888 90 92 95 96 99 99 EXERCISES ( 10 ) ........................ .. XIII . Lemma . If a ... Page 11

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**base**is known , such as BD , we can at once find AD , the remaining side of the right - angled triangle ABD . First , to find BD , Let BD = x ; .. DC = α — x . Now AD22x2 in the triangle ABD . = Again , AD2 = b2 — ( a — x ) 2 1 ... Page 13

... c + bb :: BD + DC : DC . Orc + bb :: a : DC ; .. DC = Similarly DB = ab b + c ac b + c Having thus found the segments of the

... c + bb :: BD + DC : DC . Orc + bb :: a : DC ; .. DC = Similarly DB = ab b + c ac b + c Having thus found the segments of the

**base**, we can at once find AD , for ( Euclid , VI . B ) We have BD · DC + AD2 = AB . MENSURATION OF LINES . 13.### 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'*