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 34
... contain their respective submultiples the same number of times ; and Equisubmultiples , or like submultiples , are those contained in their respective multiples the same number of times . Thus 4 and 5 are like submultiples of 8 and 10 ...
... contain their respective submultiples the same number of times ; and Equisubmultiples , or like submultiples , are those contained in their respective multiples the same number of times . Thus 4 and 5 are like submultiples of 8 and 10 ...
Página 68
... contain the same unit of measure an equal number of times . 172. 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 ...
... contain the same unit of measure an equal number of times . 172. 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 ...
Página 71
... contain four of those parts . At each point of division draw lines per- pendicular to the base ; seven rectangles will thus be formed , all equal to each other , since they have equal bases and the same altitude ( Theo . I. ) The ...
... contain four of those parts . At each point of division draw lines per- pendicular to the base ; seven rectangles will thus be formed , all equal to each other , since they have equal bases and the same altitude ( Theo . I. ) The ...
Página 82
... contain the same ratio BC : CE , we have ( Theo . IX . Bk . II . ) AC : DE :: BA : C D. Hence , the equiangular triangles BAC , CDE have their homologous sides proportional ; and consequently the two tri- angles are similar ( 172 ) ...
... contain the same ratio BC : CE , we have ( Theo . IX . Bk . II . ) AC : DE :: BA : C D. Hence , the equiangular triangles BAC , CDE have their homologous sides proportional ; and consequently the two tri- angles are similar ( 172 ) ...
Página 83
... containing these angles proportional , are similar . Let the two triangles ABC , DEF have the angle A equal to the angle D , and the sides contain- ing these angles proportional , so that AB : DE :: AC : DF ; then the triangles are ...
... containing these angles proportional , are similar . Let the two triangles ABC , DEF have the angle A equal to the angle D , and the sides contain- ing these angles proportional , so that AB : DE :: AC : DF ; then the triangles are ...
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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.