The elements of geometry, in eight books; or, First step in applied logic1874 |
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Page 134
... angles A B C and D E F. If the sides AB and BC be equal to the sides DE and E F respectively , let the two angles be applied to each other ; then , because the two angles have the same form , they will coincide with each other ...
... angles A B C and D E F. If the sides AB and BC be equal to the sides DE and E F respectively , let the two angles be applied to each other ; then , because the two angles have the same form , they will coincide with each other ...
Page 136
... angle is equal to its explement . Let A B C be a straight angle . A B Then the straight line B C is the continuation of the straight line A B ; that is , A C is a straight line . Let the angle A B C be divided into two parts by the ...
... angle is equal to its explement . Let A B C be a straight angle . A B Then the straight line B C is the continuation of the straight line A B ; that is , A C is a straight line . Let the angle A B C be divided into two parts by the ...
Page 137
... A B C be an angle equal to its explement . A B C Let BD be the prolongation of AB beyond the vertex B ; then ABD is a straight line . Let the plane containing the angle be folded upon A B D ; then all points of A B D will remain in ...
... A B C be an angle equal to its explement . A B C Let BD be the prolongation of AB beyond the vertex B ; then ABD is a straight line . Let the plane containing the angle be folded upon A B D ; then all points of A B D will remain in ...
Page 138
... angle which are not symmetric to the bisectrix , are unequally distant from ... angles , are symmetric to the common bisectrix of the angles . THEOREM 7 . The ... A B C , and let BD be its bisectrix cutting A C in D. The points A and C ...
... angle which are not symmetric to the bisectrix , are unequally distant from ... angles , are symmetric to the common bisectrix of the angles . THEOREM 7 . The ... A B C , and let BD be its bisectrix cutting A C in D. The points A and C ...
Page 139
... angle ABC [ Def . 9 ] , are symmetric to the bisectrix BD [ 6 ] ; then BD is the middle perpendicular on A C [ I. 28 ] which W. T. B. D. D COROLLARY I. Conversely , the middle perpendicular on the straight line subtending an angle ...
... angle ABC [ Def . 9 ] , are symmetric to the bisectrix BD [ 6 ] ; then BD is the middle perpendicular on A C [ I. 28 ] which W. T. B. D. D COROLLARY I. Conversely , the middle perpendicular on the straight line subtending an angle ...
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...