The elements of geometry, in eight books; or, First step in applied logic1874 |
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Σελίδα 235
... diagonal joining the adjacent vertices . 17. A lozenge , or rhombus , is a quadrangle the sides of which are equal to one another . 18. A square is a lozenge the angles of which are equal to one another . Hence , since the four angles ...
... diagonal joining the adjacent vertices . 17. A lozenge , or rhombus , is a quadrangle the sides of which are equal to one another . 18. A square is a lozenge the angles of which are equal to one another . Hence , since the four angles ...
Σελίδα 236
... diagonals to a common vertex in the same straight line , are said to be about that line , and are called diagonal parallelo- grams . 22. A trapezium is a quadrangle two sides of which , called the bases , are parallel to each other ...
... diagonals to a common vertex in the same straight line , are said to be about that line , and are called diagonal parallelo- grams . 22. A trapezium is a quadrangle two sides of which , called the bases , are parallel to each other ...
Σελίδα 237
... diagonal BD be drawn ; the quadrangle A C will be then divided into two triangles having the side B D in common . the triangles A B D and B D C have the sides A B and A D respect- ively equal to the sides CD and C B [ 29 ] , and the ...
... diagonal BD be drawn ; the quadrangle A C will be then divided into two triangles having the side B D in common . the triangles A B D and B D C have the sides A B and A D respect- ively equal to the sides CD and C B [ 29 ] , and the ...
Σελίδα 239
... diagonals bisect each other , is a parallelogram . COROLLARY II . The diagonals of a rectangle are equal to each other . COROLLARY III . The diagonals of a lozenge are the middle perpendi- cular on each other . COROLLARY IV . The ...
... diagonals bisect each other , is a parallelogram . COROLLARY II . The diagonals of a rectangle are equal to each other . COROLLARY III . The diagonals of a lozenge are the middle perpendi- cular on each other . COROLLARY IV . The ...
Σελίδα 240
... diagonals of the quadrangle . Because EF and I H are parallel to A C [ 11 i ] , they are parallel to each other [ I. 17 iii ] ; because E I and F H are parallel to B D , they are parallel to each other : therefore the quadrangle EFH I ...
... diagonals of the quadrangle . Because EF and I H are parallel to A C [ 11 i ] , they are parallel to each other [ I. 17 iii ] ; because E I and F H are parallel to B D , they are parallel to each other : therefore the quadrangle EFH I ...
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...