## The elements of geometry, in eight books; or, First step in applied logic |

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A B and C D A B C altitude angles formed base bisectrix called centre centre angle centre line chord circle circumference coincide common Const contained conversely COROLLARY II DEFINITIONS diagonals diameter difference direction divided draw drawn equally distant equivalent Eucl evident extremities formed four Geometry given given straight line greater hence homologous hypothenuse infinite inscribed intercepts intersection Inversely joined latter less lines joining magnitude mean measure meet middle line middle perpendicular middle point opposite parallel parallelograms pass perimeter perpendicular placed point of tangence polygon portions PROBLEM produced proportional prove quadrangle quantities radii radius reasoning rectangle regular polygon respectively right angles Scholium secant sector segment sides similar square straight line subtending surface symmetric tangent thence THEOREM third triangle triangle A B C unequal unit vertex vertices

### Popular passages

Page 224 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.

Page 200 - Therefore all the interior angles of the figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 228 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 143 - When a straight line standing on another straight line, makes the adjacent angles equal to one another, each of the angles is called a, right angle ; and the straight line which stands on the other is called a perpendicular to it. 11. An obtuse angle is that which is greater than a right angle. 12. An acute angle is that which is less than a right angle. 13. A term or boundary is the extremity of any thing.

Page 216 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.

Page 200 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.

Page 268 - The perimeters of two regular polygons of the same number of sides, are to each other as their homologous sides, and their areas are to each other as the squares of those sides (Prop.

Page 43 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.

Page 335 - Assuming that the areas of two triangles which have 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 382 - FLC, there -are two angles -of the one equal to two angles of the other, each to each ; and the side FC which is adjacent to the equal...