The elements of geometry, in eight books; or, First step in applied logic |
From inside the book
Page 206
An isosceles triangle has two sides equal to each other : the third side , or base , forms the angles at the base ; the opposite angular point is the apex of the triangle and is the vertex of the angle at the apex .
An isosceles triangle has two sides equal to each other : the third side , or base , forms the angles at the base ; the opposite angular point is the apex of the triangle and is the vertex of the angle at the apex .
Page 210
COROLLARY I. All the interior , or exterior , angles of an equilateral triangle , are equal to one another . COROLLARY II . If the equal sides of an isosceles triangle be produced beyond the base , they form with the base two equal ...
COROLLARY I. All the interior , or exterior , angles of an equilateral triangle , are equal to one another . COROLLARY II . If the equal sides of an isosceles triangle be produced beyond the base , they form with the base two equal ...
Page 216
Because the angles BAC and ACB are equal to each other A [ 8 ] , the angleBAC is equal to the angle ADC [ i ] ... if the base of an isosceles triangle be equal to the mean of one of the equal sides , each angle at the base is double of ...
Because the angles BAC and ACB are equal to each other A [ 8 ] , the angleBAC is equal to the angle ADC [ i ] ... if the base of an isosceles triangle be equal to the mean of one of the equal sides , each angle at the base is double of ...
Page 219
therefore the triangles ABC and DEF are equal to each other , W.W.T. B. D. COROLLARY I. If two triangles have two ... If two isosceles triangles have the angle at the apex , or an angle at the base , and the opposite side of the one ...
therefore the triangles ABC and DEF are equal to each other , W.W.T. B. D. COROLLARY I. If two triangles have two ... If two isosceles triangles have the angle at the apex , or an angle at the base , and the opposite side of the one ...
Page 231
Two isosceles triangles which have the base and one side of the one , proportional to the base and one side of the ... If two triangles have one angle of the one equal to one angle of the other , if the sides forming another angle be ...
Two isosceles triangles which have the base and one side of the one , proportional to the base and one side of the ... If two triangles have one angle of the one equal to one angle of the other , if the sides forming another angle be ...
What people are saying - Write a review
We haven't found any reviews in the usual places.
Common terms and phrases
A B and C D A B C altitude angle A B C angles formed base bisectrix called centre centre line chord circle circumference coincide common Const contained conversely COROLLARY II DEFINITIONS diagonals diameter difference direction divided draw drawn equally distant equivalent Eucl extremities formed four Geometry given given straight line greater hence homologous hypothenuse infinite inscribed intercepts Inversely joined latter less Let A B lines joining magnitude mean measure meet middle perpendicular opposite parallel parallelograms pass perimeter perpendicular placed point of tangence polygon portion PROBLEM produced proportional 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...
Bibliographic information
| Title | The elements of geometry, in eight books; or, First step in applied logic |
| Author | L J V. Gerard |
| Published | 1874 |
| Original from | Oxford University |
| Digitized | 7 Sep 2006 |
| Export Citation | BiBTeX EndNote RefMan |