New Elementary Geometry: With Practical Applications : a Shorter Course Upon the Basis of the Larger WorkRobert S. Davis & Company, 1874 - 176 páginas |
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Página 54
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; therefore it must be A D ; hence we have , Angle A C B : angle A CD :: arc A B : arc A D. 155. Cor . 1. An angle having its vertex at the center ...
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; therefore it must be A D ; hence we have , Angle A C B : angle A CD :: arc A B : arc A D. 155. Cor . 1. An angle having its vertex at the center ...
Página 68
... Similar Figures are such as have the angles of the one equal to those of the other , each to each , and the sides con- taining the equal angles proportional . 173. Equivalent Figures are such as have equal areas . Figures may be ...
... Similar Figures are such as have the angles of the one equal to those of the other , each to each , and the sides con- taining the equal angles proportional . 173. Equivalent Figures are such as have equal areas . Figures may be ...
Página 81
... similar . Let the two triangles A B C , D CE be equiangular ; the angle B A C being equal to the angle CD E , the angle A B C to the angle DCE , and the angle A CB to the angle D E C , then the homologous sides will be propor- B tional ...
... similar . Let the two triangles A B C , D CE be equiangular ; the angle B A C being equal to the angle CD E , the angle A B C to the angle DCE , and the angle A CB to the angle D E C , then the homologous sides will be propor- B tional ...
Página 82
... similar ; since the third angles will also be equal , and the two triangles be equiangular . 206. Scholium . In similar triangles , the homologous sides are opposite to the equal angles ; thus the angle A CB being equal to D E C , the ...
... similar ; since the third angles will also be equal , and the two triangles be equiangular . 206. Scholium . In similar triangles , the homologous sides are opposite to the equal angles ; thus the angle A CB being equal to D E C , the ...
Página 83
... 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 proportional , are similar . Let the two triangles A B C , DEF have the angle A equal to ...
... 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 proportional , are similar . Let the two triangles A B C , DEF have the angle A equal to ...
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New Elementary Geometry with Practical Applications Benjamin Greenleaf Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD ABCDEF alti altitude Theo angle A CD axis base multiplied bisect chord circum circumference circumscribed cone convex surface D E F diagonal diameter divided ELEMENTARY ALGEBRA ellipse entire surface equal Theo equivalent formed frustum greater GREENLEAF'S half the sum hence homologous homologous sides hypothenuse inches inscribed circle inscribed square intersection magnitudes mean proportional measured by half Metric System number of sides parallelogram parallelopipedon perimeter perpendicular prism PROBLEM quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo right pyramid rods Scholium SCHOOLS sector semicircle side A B side B C similar slant hight solid sphere is equal spherical square described square feet square root tangent THEOREM third triangles A B C triangular triangular prism tude vertex
Pasajes populares
Página 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.
Página 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.
Página 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.
Página 61 - At a point in a given straight line to make an angle equal to a given angle.
Página 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Página 93 - The side of a regular hexagon inscribed in a circle is equal to the radius of the circle.
Página 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.
Página 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...
Página 88 - FIK are similar ; hence the similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.
Página 124 - But the solidity of each triangular prism is equal to the product of its base by its altitude ; and.