An Elementary Geometry |
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Page 10
... triangle , as DEF , in which DE = EF , the third side DF is always considered the base . THEOREM VII . 33. The sum of the angles of a triangle is equal to two right angles . Let A B C be a triangle ; the sum of its three angles , A , B ...
... triangle , as DEF , in which DE = EF , the third side DF is always considered the base . THEOREM VII . 33. The sum of the angles of a triangle is equal to two right angles . Let A B C be a triangle ; the sum of its three angles , A , B ...
Page 11
... triangle there can be but one right angle , or one obtuse angle . 37. Cor . 4. In a right triangle the sum of the ... ABC , DEF , let the side A B B E equal DE , AC equal DF , and the angle A equal the angle D ; then the triangle ABC is ...
... triangle there can be but one right angle , or one obtuse angle . 37. Cor . 4. In a right triangle the sum of the ... ABC , DEF , let the side A B B E equal DE , AC equal DF , and the angle A equal the angle D ; then the triangle ABC is ...
Page 12
... triangles are equal in all respects . In the triangles ABC and DEF , let the angle A equal the angle D , the angle C equal the angle F , and the side A C equal DF ; then the triangle B E خ C D ABC is equal in all respects to the triangle ...
... triangles are equal in all respects . In the triangles ABC and DEF , let the angle A equal the angle D , the angle C equal the angle F , and the side A C equal DF ; then the triangle B E خ C D ABC is equal in all respects to the triangle ...
Page 13
... triangle are equal , the sides opposite are also equal . A D B In the triangle ABC , let the angle A equal the angle C ; then A B is equal to BC . For if AB is not equal to BC , suppose AB to be greater than BC , and from A B cut off ...
... triangle are equal , the sides opposite are also equal . A D B In the triangle ABC , let the angle A equal the angle C ; then A B is equal to BC . For if AB is not equal to BC , suppose AB to be greater than BC , and from A B cut off ...
Page 14
... ABC C. THEOREM XIII . 48. Two triangles mutually equilateral are equal in all respects . Let the triangle ABC have AB , BC , CA respec- - tively equal to AD , DC , CA of the triangle ADC ; then ABC is equal in all respects to ADC . Place ...
... ABC C. THEOREM XIII . 48. Two triangles mutually equilateral are equal in all respects . Let the triangle ABC have AB , BC , CA respec- - tively equal to AD , DC , CA of the triangle ADC ; then ABC is equal in all respects to ADC . Place ...
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Common terms and phrases
A B C ABCD adjacent altitude angle ABC apothem arcs A B base and altitude bisect centre chord circ circumference cone construct the triangle convex surface Corollary cube cylinder diagonals diameter distance divided dodecagon EATON'S equal altitudes equally distant equiangular equilateral feet frustum given angle given circle given line given point given side given square half the arc hexagon homologous sides hypothenuse included angle infinite number inscribed internal angles intersection isosceles triangle Let ABCDEF line joining lines A B measured by half number of sides opposite sides parallel planes parallelogram parallelopiped perimeter perpendicular plane parallel quadrilateral radii radius ratio rectangle regular polygon respectively equal rhombus right angles right prism right pyramid right triangle Scholium secant segment similar triangles slant height sphere tangent THEOREM VII trapezoid triangle ABC vertex
Popular passages
Page 25 - Four quantities are in proportion when the ratio of the first to the second is equal to the ratio of the third to the fourth.
Page 30 - If any number of quantities are proportional, any antecedent is to its consequent as the sum of all the antecedents is to the sum of all the consequents. Let a : b = c : d = e :f Now ab = ab (1) and by Theorem I.
Page 27 - If the product of two quantities is equal to the product of two others, the...
Page 43 - The area of a regular polygon is equal to half the product of its perimeter and apothem.
Page 11 - If two triangles have two sides, and the included angle of the one equal to two sides and the included angle of the other, each to each, the two triangles are equal in all respects.
Page 23 - If two triangles have two sides of one respectively equal to two sides of the other, but the third sides unequal...
Page 20 - ... polygon, is equal to twice as many right angles as the polygon has sides minus two.
Page 49 - A Circle is a plane figure bounded by a curved line every point of which is equally distant from a point within called the center.
Page 70 - A right cylinder is a solid described by the revolution of a rectangle about one of its sides.
Page 64 - DEFINITIONS. 1 . A straight line is perpendicular to a plane, when it is perpendicular to every straight line of the plane which it meets.