## Mensuration of lines, areas, surfaces, and volumes |

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### Common terms and phrases

15 feet 9 feet 9 inches added angle ANSWERS balk base body breadth called centre of gravity chord circle circumference column common interval concentric cone cubic feet curve cylinder describe diameter displacement distance divided draw ellipse equal EXAMPLES feet 6 inches feet 9 field figure find its volume find the area Find the volume foot formula given half height horizontal planes hour immersed inclined join length means measured middle miles multiply ordinates parabola perpendicular pitch placed Plan position PROB PROBLEM progression quantities quotient radius range ratio respectively result rise screw segment ship sides Simpson's rule slip solid span sphere square straight line surface tons transverse triangle vessel volume and surface wall water-line

### Popular passages

Page xv - LET it be granted that a straight line may be drawn from any one point to any other point.

Page xiii - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.

Page xii - A plane superficies is that in which any two points being taken, the straight line between them lies wholly in that superficies. VIII. " A plane angle is the inclination of two lines to one " another in a plane, which meet together, but are not

Page xv - An oblong is that which has all its angles right angles, but has not all its sides equal.

Page xii - When several angles are at one point B, any one of them is expressed by three letters, of which the letter that is at vertex of the angle, that is, at the point in which the straight lines that contain the angle meet one another, is put between the other two letters, and one of these two is somewhere upon one of those straight...

Page xii - A plane rectilineal angle is the inclination of two straight lines to one another, -which meet together, but are not in the same straight line.

Page xiv - Of three-sided figures, an equilateral triangle is that which has three equal sides.

Page xvi - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Page xiii - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle. 17. A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page xvi - Magnitudes which coincide with one another, that is, which exactly fill the same space, are equal to one another.