New Elementary Geometry, with Practical ApplicationsR. S. Davis & Company, 1875 - 176 páginas |
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Página 23
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal . Let the two right - angled A triangles A B BOOK I. 23.
... hypothenuse and a side of the one equal to the hypothenuse and a side of the other , each to each , the triangles are equal . Let the two right - angled A triangles A B BOOK I. 23.
Página 24
... hypothenuse A C equal to D F , and the side AB equal to DE ; then will the triangle A B C be equal B G to the triangle DE F. D CE The two triangles are evidently equal , if the sides BC and EF are equal ( Theo . XIII . ) . If it be ...
... hypothenuse A C equal to D F , and the side AB equal to DE ; then will the triangle A B C be equal B G to the triangle DE F. D CE The two triangles are evidently equal , if the sides BC and EF are equal ( Theo . XIII . ) . If it be ...
Página 76
... on the half A B. 194. Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) 2 = a2 + 2ab + b2 . EH D G I A B C THEOREM IX . 195. The square described on the hypothenuse 76 ELEMENTARY GEOMETRY .
... on the half A B. 194. Scholium . This proposition is equivalent to the algebraical formula , ( a + b ) 2 = a2 + 2ab + b2 . EH D G I A B C THEOREM IX . 195. The square described on the hypothenuse 76 ELEMENTARY GEOMETRY .
Página 77
... hypothenuse BC will be equivalent to the sum of the squares on the sides BA , A C. On B C describe the square BCG F , and on A B , A C the squares ABHL , A CIK ; pro- duce FB to N , HL and I K to M ; and through A draw EDA parallel to ...
... hypothenuse BC will be equivalent to the sum of the squares on the sides BA , A C. On B C describe the square BCG F , and on A B , A C the squares ABHL , A CIK ; pro- duce FB to N , HL and I K to M ; and through A draw EDA parallel to ...
Página 78
... hypothenuse diminished by the square of the other side ; thus , A B3 is equivalent to B C2 — A C2 . - 197. Cor . 2. The square described on the diagonal of a square is equivalent to double the square described on a side . For let ABCD ...
... hypothenuse diminished by the square of the other side ; thus , A B3 is equivalent to B C2 — A C2 . - 197. Cor . 2. The square described on the diagonal of a square is equivalent to double the square described on a side . For let ABCD ...
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New Elementary Geometry with Practical Applications Benjamin Greenleaf Sin vista previa disponible - 2016 |
Términos y frases comunes
ABCD ABCDEF alternate angles altitude angles A CD antecedent arc A B Arithmetics B A C base multiplied bisect circle circumference cone convex surface cylinder D E F diagonal diameter divided draw the straight Elementary Algebra equal and parallel equal angles equal bases equal Theo equiangular equivalent formed frustum given straight line greater half the sum homologous sides hypothenuse inches included angle inscribed angle inscribed circle interior angles intersection line CD magnitudes mean proportional measured by half number of sides parallelogram parallelopipedon perimeter perpendicular prism PROBLEM quadrilateral radii radius ratio rectangle rectangular regular polygon Required the area rhombus right angles Theo Scholium School secant line side A B side B C slant hight Solid sphere square described tangent THEOREM triangles A B C triangular prism vertex
Pasajes populares
Página 22 - If two triangles have two sides of the one equal to two sides of the...
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 61 - At a point in a given straight line to make an angle equal to a given angle.
Página 47 - 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 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 126 - The volume of any prism is equal to the product of its base by its altitude. Let V denote the volume, B the base, and H the altitude of the prism DA'.
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.
Página 26 - If a straight line falling upon two other straight lines, make the exterior angle equal to the interior and opposite upon the same side of the line...
Página 41 - 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.