New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger Work |
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Page 29
... equiangular figure of more than four sides , each angle is greater than a right angle ; thus , in a regular pentagon , each angle is equal to one and one fifth right angles ; in a regular hexagon , to one and one third right angles ...
... equiangular figure of more than four sides , each angle is greater than a right angle ; thus , in a regular pentagon , each angle is equal to one and one fifth right angles ; in a regular hexagon , to one and one third right angles ...
Page 33
... equiangular . 5. Any side of a triangle is less than the sum of the other two . 6. The difference between any two sides of a triangle is less than the other side . 7. The side in a right - angled triangle opposite the right an- gle is ...
... equiangular . 5. Any side of a triangle is less than the sum of the other two . 6. The difference between any two sides of a triangle is less than the other side . 7. The side in a right - angled triangle opposite the right an- gle is ...
Page 81
... Equiangular triangles have their homologous sides proportional , and are similar . Let the two triangles ABC , DCE be equiangular ; the angle BAC being equal to the angle CDE , the angle ABC to the angle DCE , and the angle ACB to ...
... Equiangular triangles have their homologous sides proportional , and are similar . Let the two triangles ABC , DCE be equiangular ; the angle BAC being equal to the angle CDE , the angle ABC to the angle DCE , and the angle ACB to ...
Page 82
... equiangular triangles BAC , C D E have their homologous sides proportional ; and consequently the two tri- angles are similar ( 172 ) . 205. Cor . Two triangles having two angles of the one equal to two angles of the other , each to ...
... equiangular triangles BAC , C D E have their homologous sides proportional ; and consequently the two tri- angles are similar ( 172 ) . 205. Cor . Two triangles having two angles of the one equal to two angles of the other , each to ...
Page 83
... equiangular with the triangle ABC ; hence the triangles DEF , ABC are also equiangular and similar . THEOREM XV . 208. Two triangles , which have an angle of the one equal to an angle of the other , and the sides containing these angles ...
... equiangular with the triangle ABC ; hence the triangles DEF , ABC are also equiangular and similar . THEOREM XV . 208. Two triangles , which have an angle of the one equal to an angle of the other , and the sides containing these angles ...
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A B C A B equal ABCD ABCDEF adjacent angles allel alternate angles altitude angle ACD angle BAC antecedent base multiplied bases ABC bisect chord circumference cone consequently convex surface cylinder diagonal diameter divided draw the straight equal and parallel equal angles equal bases equal Theo equiangular equivalent feet formed four right angles frustum given straight line greater Greenleaf's half the sum homologous sides hypothenuse included angle inscribed angle inscribed circle interior angles intersection Let ABC line CD magnitudes mean proportional measured by half meet number of sides opposite parallelogram parallelopipedon perimeter perpendicular polyedron prism quadrilateral radii radius ratio rectangle regular polygon rhombus right angles Theo Scholium secant line side A B side BC slant hight Solid sphere square described tangent THEOREM third triangles ABC triangular triangular prism vertex volume
Popular passages
Page 23 - 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 29 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 83 - Two triangles, which have an angle of the one equal to an angle of the other, and the sides containing these angles proportional, are similar.
Page 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Page 61 - At a point in a given straight line to make an angle equal to a given angle.
Page 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Page 62 - Through a given point to draw a straight line parallel to a given straight line, Let A be the given point, and BC the given straight line : it is required to draw through the point A a straight line parallel to BC.
Page 117 - If two angles not in the same plane have their sides parallel and lying in the same direction, these angles will be equal, and their planes will be parallel. Let...
Page 100 - The circumferences of circles are to each other as their radii, and their areas are to each other as the squares of their radii. Let C denote the circumference of one of ^ the circles, R its radius OA, A its area; and let C...
Page 88 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.