## Plane and Solid Geometry |

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### Common terms and phrases

ABCD altitude approaches axis base bisector bisects called chord circle circumference circumscribed coincide common cone Construct contained corresponding cubes cylinder Data denote diagonals diameter difference dihedral angles direction distance divide Draw drawn equal equidistant equilateral triangle equivalent extremities faces figure Find formed four frustum given given line given point greater half Hence homologous included inscribed interior angles intersecting isosceles triangle joining length less limit mean measure meet middle point opposite sides parallel parallel lines parallelogram parallelopiped perimeter perpendicular plane polygon polyhedron prism produced Proof proportional Proposition prove pyramid quadrilateral radii radius ratio rect reference regular polygon Represent respectively right angles right triangle segment sides similar sphere spherical triangle square straight line student surface symmetrical tangent Theorem third triangle triangular trihedral vertex vertical angle volume

### Popular passages

Page 103 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Page 147 - Sines that the bisector of an angle of a triangle divides the opposite side into parts proportional to the adjacent sides.

Page 65 - The line joining the middle points of two sides of a triangle is parallel to the third side and equal to half of the third side.

Page 45 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 62 - From 56 and 57 the pupils should learn that two triangles are equal in every respect (a) when two sides and the included angle of one are equal to two sides and the included angle of the other...

Page 59 - If the opposite sides of a quadrilateral are equal, the figure is a parallelogram.

Page 81 - A circle is a plane figure bounded by a curved line, every point of which is equally distant from a point within called the center.

Page 45 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 31 - If two parallel lines are cut by a third straight line, the sum of the two interior angles on the same side of the secant line is equal to two right angles.

Page 88 - In the same circle, or in equal circles, equal chords are equally distant from the center; and, conversely, chords equally distant from the center are equal.