## Essentials of Geometry |

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A B C adjacent altitude axis base bisect called centre chord circle circumference coincide common cone construct cylinder DEFINITIONS denote describe diagonals diameter difference direction distance divided draw drawn equal equally distant equiangular equilateral EXERCISES extremities faces fall feet figure four frustum given given line greater half height Hence homologous hypothesis inscribed intersect isosceles joining lateral length less lune mean measure meet multiplied oblique parallel parallelogram pass perimeter perpendicular plane polygon portion position prism Prob PROBLEM proportional Prove pyramid quantities QUERIES radii radius ratio rectangle regular polygon right angles Scholium segments sides similar sphere spherical triangle square straight line Suppose surface tangent THEOREM third triangle unit vertex vertices VIII volume

### Popular passages

Page 18 - if two triangles have two sides of the one equal to two sides of the...

Page 110 - In any triangle the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon it.

Page 13 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.

Page 107 - If two triangles have two sides and the included angle of the one equal to two sides and the included angle of the other, each to each, they are equal in all their parts.

Page 24 - 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 38 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.

Page 42 - If the product of two quantities is equal to the product of two others, two of them may be made the means, and the other two the extremes of a proportion. Let bc=ad.

Page 232 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.

Page 14 - In an isosceles triangle the angles opposite the equal sides are equal.

Page x - AXIOM is a self-evident truth ; such as, — 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. 3. If equals be taken from equals, the remainders will be equal. 4. If equals be added to unequals, the sums will be unequal.