## Plane and Solid Geometry |

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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 isosceles joining length less limit locus measured meet mid-point opposite parallel parallel lines parallelepiped parallelogram passes perimeter perpendicular placed plane plane MN polygon polyhedron Post 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 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 356 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.

Page 186 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.

Page 148 - 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 52 - 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 31 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 75 - 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. Given A ABC and A'B'C...

Page 49 - 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.

Page 22 - The following are the most important axioms used in geometry: 1. If equals are added to equals the sums are equal. 2. If equals are subtracted from equals the remainders are equal. 3. If equals are multiplied by equals the products are equal. 4. If equals are divided by equals the quotients are equal.

Page 209 - The square constructed upon the sum of two lines is equivalent to the sum of the squares constructed upon these two lines, increased by twice the rectangle of these lines.