## The Elements of Plane and Solid Geometry: With Numerous Exercises |

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### Common terms and phrases

ABCD adjacent altitude base bisect bisector called centre chord circle circumference circumscribed coincide common cone Cons construct contains cylinder describe diagonals diameter diedral angle difference distance divided draw drawn edges equal equally distant equilateral equivalent EXERCISES faces feet figure Find formed four frustum given given point given straight line greater half height homologous inches included inscribed intersection isosceles Join lateral area length less limit mean measured meet middle point parallel parallelogram parallelopiped pass perimeter perpendicular plane polygon prism Problem produced Proof proportional Proposition prove pyramid quantities radii radius ratio rectangle regular polygon respectively right angles segment sides similar sphere square straight line surface tangent Theorem third triangle vertex vertices volume

### Popular passages

Page 74 - A circle is a plane figure bounded by a curved line, called the circumference, every point of which is equally distant from a point within called the center.

Page 188 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.

Page 45 - If two triangles have two sides of the one equal respectively to two sides of the other, but the included angle of the first greater than the included angle of the second, then the third side of the first is greater than the third side of the second. Hyp. In A ABC and A'B'C' AB = A'B'; AC = A'C'; ZA>ZA'.

Page 137 - Terms of the proportion. The first and fourth terms are called the Extremes, and the second and third the Means.

Page 12 - AXIOMS. 1. Things which are equal to the same thing are equal to each other. 2. If equals be added to equals, the sums will be equal.

Page 206 - To divide a given straight line into two parts, so that the rectangle contained by the whole and one of the parts, shall be equal to the square on the other part.

Page 97 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.

Page 334 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.

Page 12 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 253 - Equal oblique lines from a point to a plane meet the plane at equal distances from the foot of the perpendicular ; and of two unequal oblique lines the greater meets the plane at the greater distance from the foot of the perpendicular.