Book 11
DEFINITIONS.
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1
A solid is that which has length, breadth, and depth.
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2
An extremity of a solid is a surface.
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3
A straight line is at right angles to a plane, when it makes right angles with all the straight lines which meet it and are in the plane.
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4
A plane is at right angles to a plane when the straight lines drawn, in one of the planes, at right angles to the common section of the planes are at right angles to the remaining plane.
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5
The inclination of a straight line to a plane is, assuming a perpendicular drawn from the extremity of the straight line which is elevated above the plane to the plane, and a straight line joined from the point thus arising to the extremity of the straight line which is in the plane, the angle contained by the straight line so drawn and the straight line standing up.
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6
The inclination of a plane to a plane is the acute angle contained by the straight lines drawn at right angles to the common section at the same point, one in each of the planes.
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7
A plane is said to be similarly inclined to a plane as another is to another when the said angles of the inclinations are equal to one another.
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8
Parallel planes are those which do not meet.
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9
Similar solid figures are those contained by similar planes equal in multitude.
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10
Equal and similar solid figures are those contained by similar planes equal in multitude and in magnitude.
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11
A solid angle is the inclination constituted by more than two lines which meet one another and are not in the same surface, towards all the lines.
11
Otherwise: A solid angle is that which is contained by more than two plane angles which are not in the same plane and are constructed to one point.
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12
A pyramid is a solid figure, contained by planes, which is constructed from one plane to one point.
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13
A prism is a solid figure contained by planes two of which, namely those which are opposite, are equal, similar and parallel, while the rest are parallelograms.
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