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

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### Common terms and phrases

15 feet 9 feet 9 inches acre angle balk base body breadth bridge called centre of gravity chord circle circumference column common interval cone cubic feet curve cutting cylinder describe diameter difference displacement distance divide draw ellipse equal EXAMPLES feet 6 inches feet 9 field figure find its volume find the area Find the centre Find the volume foot formula given half height hour immersed inclined join length means measured miles multiply ordinates parabola parallel perpendicular pitch placed plane position PROBLEM radius range ratio respectively result right angles rise screw Section segment ship sides Simpson's rule slip solid span sphere square straight line surface three sides tons triangle versed sine vertical vessel volume and surface water-line yards

### Popular passages

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

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

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

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