## Plane and Solid Geometry |

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### Common terms and phrases

ABCD altitude base bisector bisects called chord circle circular circumscribed coincide common cone congruent construct COROLLARY corresponding cylinder describe diagonal diameter difference dihedral angles distance divide draw drawn edges equal equidistant equivalent EXERCISE external faces figure Find follows formed four frustum geometry given line given point greater half height Hence included inscribed intersecting joining lateral length less limit locus measured meet mid-point opposite parallel parallel lines parallelepiped parallelogram pass perimeter perpendicular placed plane plane MN polygon polyhedron prism PROBLEM Proof proportional PROPOSITION prove pyramid quadrilateral radii radius ratio rectangle regular regular polygon relation respectively right angle segments shown sides similar solid sphere square straight line Suppose surface symmetric tangent THEOREM third triangle triangle ABC vertex vertices volume

### Popular passages

Page 1 - Pythagorean theorem, which states that the square of the hypotenuse of a right triangle equals the sum of the squares of the other two sides.

Page 292 - The line joining the mid-points of two sides of a triangle is parallel to the third side, and equal to half the third side.

Page 360 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.

Page 201 - 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 54 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.

Page 190 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 152 - If the product of two quantities is equal to the product of two others, either two may be made the extremes of a proportion and the other two the means.

Page 162 - The bisector of an angle of a triangle divides the opposite side into segments which are proportional to the adjacent sides.

Page 100 - In the same circle or in equal circles, if two chords are unequal, they are unequally distant from the center, and the greater chord is at the less distance.

Page 51 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.