New Elementary Geometry: With Practical Applications ; a Shorter Course Upon the Basis of the Larger WorkR.S. Davis & Company, 1873 - 176 páginas |
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Página 45
... Sector of a circle is the part of a circle included between an D A B C E F G arc , and the two radii drawn to the extremities of the arc ; as the surface included between the arc AD , and the two radii CA , CD . 128. A Secant to a ...
... Sector of a circle is the part of a circle included between an D A B C E F G arc , and the two radii drawn to the extremities of the arc ; as the surface included between the arc AD , and the two radii CA , CD . 128. A Secant to a ...
Página 55
... Sectors taken in the same circle , or in equal circles , are to each other as their arcs ; for sectors are equal when their angles are so , and therefore are in all re- spects proportional to their angles . THEOREM X. 160. An inscribed ...
... Sectors taken in the same circle , or in equal circles , are to each other as their arcs ; for sectors are equal when their angles are so , and therefore are in all re- spects proportional to their angles . THEOREM X. 160. An inscribed ...
Página 68
... Sectors are such as corre- spond to equal angles at the centers of the circles . Thus , if the angles A and E are equal , the arc BC will be similar to the arc FG ; the ... sector A B BOOK IV AREAS AND RELATIONS OF PLANE FIGURES Definitions.
... Sectors are such as corre- spond to equal angles at the centers of the circles . Thus , if the angles A and E are equal , the arc BC will be similar to the arc FG ; the ... sector A B BOOK IV AREAS AND RELATIONS OF PLANE FIGURES Definitions.
Página 69
... sector A B C to the sector EFG . 176. The Altitude of a Triangle is the perpendicular , which measures the distance of any one of its vertices from the opposite side taken as a base ; as the perpendicular A D let fall on the base BC in ...
... sector A B C to the sector EFG . 176. The Altitude of a Triangle is the perpendicular , which measures the distance of any one of its vertices from the opposite side taken as a base ; as the perpendicular A D let fall on the base BC in ...
Página 101
... we have A : A ' :: 4 R2 : 4 r2 . THEOREM XXXI . 241. Similar arcs are to each other as their radii ; and similar sectors are to each other as the squares of their radii . Let AB , DE be similar arcs ; A ACB 9 * BOOK IV . 101.
... we have A : A ' :: 4 R2 : 4 r2 . THEOREM XXXI . 241. Similar arcs are to each other as their radii ; and similar sectors are to each other as the squares of their radii . Let AB , DE be similar arcs ; A ACB 9 * BOOK IV . 101.
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New Elementary Geometry with Practical Applications Benjamin Greenleaf Sin vista previa disponible - 2016 |
Términos y frases comunes
A B C D ABCD ABCDEF alti altitude altitude Theo angle A CD axis base multiplied bisect chord circumference circumscribed cone convex surface diagonal diameter divided Elementary Algebra ellipse entire surface equal Theo equivalent frustum greater GREENLEAF'S NEW MATHEMATICAL Greenleaf's New Series half the sum hence homologous homologous sides hypothenuse inches inscribed circle magnitudes MATHEMATICAL SERIES mean proportional measured by half number of sides parallelogram parallelopipedon Parker's Exercises perimeter perpendicular prism PROBLEM radii radius ratio rectangle rectangular regular polygon Required the area Required the volume rhombus right angles Theo rods Scholium School secant line side A B side B C similar slant hight solid sphere is equal spherical square described square feet THEOREM triangles A B C triangular triangular prism vertex zoid
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 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 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 85 - If in a right triangle a perpendicular is drawn from the vertex of the right angle to the hypotenuse : I.
Página 61 - At a point in a given straight line to make an angle equal to a given angle.
Página 57 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
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 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...
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 - Similar polygons may be divided into the same number of triangles similar each to each, and similarly situated.