The elements of geometry, in eight books; or, First step in applied logic1874 |
From inside the book
Results 1-5 of 36
Page 90
... secant thereto . A secant is necessarily infinite on each side of the circumference to which it is secant . However , if several secants be drawn to a circumference from a point without it , the length of each of them is reckoned from ...
... secant thereto . A secant is necessarily infinite on each side of the circumference to which it is secant . However , if several secants be drawn to a circumference from a point without it , the length of each of them is reckoned from ...
Page 92
... secants to it . COROLLARY V. If two equal secants be drawn to a circumference from a point without it , that point , the middle points of the convex and concave arcs and of their chords , are , with the centre of the circumfer- ence ...
... secants to it . COROLLARY V. If two equal secants be drawn to a circumference from a point without it , that point , the middle points of the convex and concave arcs and of their chords , are , with the centre of the circumfer- ence ...
Page 93
... secants passing through their extremities are not parallel to each other . COROLLARY I. Conversely , if two arcs of a circumference be equal to each other , the chords joining their extremities without crossing each other , are parallel ...
... secants passing through their extremities are not parallel to each other . COROLLARY I. Conversely , if two arcs of a circumference be equal to each other , the chords joining their extremities without crossing each other , are parallel ...
Page 94
... secant is oblique to the radius terminating at a point of section . COROLLARY . From a point without a circumference there may be two tangents thereto . THEOREM 55 . Conversely , a tangent to a circumference is perpendicular to the ...
... secant is oblique to the radius terminating at a point of section . COROLLARY . From a point without a circumference there may be two tangents thereto . THEOREM 55 . Conversely , a tangent to a circumference is perpendicular to the ...
Page 95
... secant , or tangent , are equal to each other . THEOREM 56 . The perpendicular raised on a tangent through the point of tangence passes through the centre of the circumference . Let A B be a tangent at the point B to the circumference O ...
... secant , or tangent , are equal to each other . THEOREM 56 . The perpendicular raised on a tangent through the point of tangence passes through the centre of the circumference . Let A B be a tangent at the point B to the circumference O ...
Common terms and phrases
A B and C D A B C and D E F adjacent angles adjacent sides altitude angle A B C angle ABC angles formed apothem bisect bisectrix centre angle centre line chord circular segment coincide Const Conversely COROLLARY II diagonals diameter divided equal angles equal circumferences equal to half equally distant equilateral equilateral polygon equivalent Eucl extremities given straight line greater homologous hypothenuse inscribed angle intercepts intersection isosceles trapezium isosceles triangle Let A B C magnitude middle line middle perpendicular middle point parallel parallelogram perimeter plane figure point H point of tangence points of section portions produced quadrangle quantities radii radius reasoning would prove rectangle regular polygon right-angled triangle Scholium segment sides A B square straight angle symmetric points tangent THEOREM transversal trapezium triangle A B C unequal vertex W. W. T. B. D. COROLLARY W. W. T. B. D. Inversely
Popular passages
Page 226 - 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 202 - 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 230 - 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 218 - 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 202 - 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...