## Essentials of Geometry |

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A B and C D A B C D A B D A C B adjacent angles angle equal apothem bisect centre chord circumference coincide convex surface cylinder D E F diagonals diameter distance divided draw drawn equal altitudes equal bases equal circles equally distant equiangular EXERCISES extremities feet frustum generatrix given angle given circle given line given point greater hence homologous sides hypotenuse hypothesis included angle inscribed angle interior angles isosceles triangle Let A B number of sides oblique parallel lines parallelogram parallelopiped perimeter perpendicular plane prism Prob pyramid Q. E. D. Cor quadrilateral QUERIES radii radius ratio rectangle reductio ad absurdum regular polygon right cone right triangle Scholium secant segments similar slant height sphere spherical triangle straight line tangent THEOREM VII vertex vertices VIII

### Popular passages

Page 24 - if two triangles have two sides of the one equal to two sides of the...

Page 118 - 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 19 - 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 115 - 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 30 - 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 44 - If two sides of a quadrilateral are equal and parallel, the figure is a parallelogram.

Page 48 - 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 256 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.

Page 20 - In an isosceles triangle the angles opposite the equal sides are equal.

Page 6 - 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.