The elements of geometry, in eight books; or, First step in applied logic1874 |
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Σελίδα 134
... bisectrix of an angle is the straight line which divides the angle into two equal parts . It follows from the definition of the angle that the bisectrix passes through the vertex . THEOREM 1 . Similar angles are equal to each other ...
... bisectrix of an angle is the straight line which divides the angle into two equal parts . It follows from the definition of the angle that the bisectrix passes through the vertex . THEOREM 1 . Similar angles are equal to each other ...
Σελίδα 136
... bisectrix of an angle bisects its vertical and its explement . COROLLARY III . The prolongations of the sides of a projecting angle are outside the angle , and conversely . COROLLARY IV . The prolongations of the sides of a receding ...
... bisectrix of an angle bisects its vertical and its explement . COROLLARY III . The prolongations of the sides of a projecting angle are outside the angle , and conversely . COROLLARY IV . The prolongations of the sides of a receding ...
Σελίδα 137
... bisectrix of the angle . Let the points A and C of the angle A B C , be equally distant from the vertex B. Let BD be the bisectrix of the angle ABC , and let the plane containing the angle be folded upon BD . Because the angles A BD and ...
... bisectrix of the angle . Let the points A and C of the angle A B C , be equally distant from the vertex B. Let BD be the bisectrix of the angle ABC , and let the plane containing the angle be folded upon BD . Because the angles A BD and ...
Σελίδα 138
... bisectrix , are unequally distant from the vertex . COROLLARY I. Conversely , two points of the sides of an angle which are symmetric to the bisectrix are symmetric points of the angle . COROLLARY II . The portions of the sides of an ...
... bisectrix , are unequally distant from the vertex . COROLLARY I. Conversely , two points of the sides of an angle which are symmetric to the bisectrix are symmetric points of the angle . COROLLARY II . The portions of the sides of an ...
Σελίδα 139
... bisectrix of the angle . COROLLARY II . The perpendicular drawn from the vertex on the straight line subtending an angle symmetrically , bisects the latter and also the angle . COROLLARY III . The straight line perpendicular to the ...
... bisectrix of the angle . COROLLARY II . The perpendicular drawn from the vertex on the straight line subtending an angle symmetrically , bisects the latter and also the angle . COROLLARY III . The straight line perpendicular to the ...
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 202 - The measure of an exterior angle of a triangle is equal to the sum of the measures of the two remote interior angles.
Σελίδα 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.
Σελίδα 43 - The projection of a point on a plane is the foot of the perpendicular drawn from the point to the plane.
Σελίδα 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...
Σελίδα 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...