Elements of Geometry: With Practical Applications to MensurationLeach, Shewell and Sanborn, 1863 - 320 páginas |
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Página 71
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; therefore it must be AD ; hence we have , Angle ACB angle A CD :: arc A B : arc AD . 198. Scholium 1. Since the angle at the center of a circle ...
... similar , it may be shown that the fourth term of the proportion cannot be less than AD ; therefore it must be AD ; hence we have , Angle ACB angle A CD :: arc A B : arc AD . 198. Scholium 1. Since the angle at the center of a circle ...
Página 76
... SIMILAR FIGURES are such as have the angles of the one equal to those of the other , each to each , and the sides containing the equal angles proportional . 211. 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 containing the equal angles proportional . 211. EQUIVALENT FIGURES are such as have equal areas . Figures may be ...
Página 77
... similar to the arc FG ; the segment BDC to the segment FHG , and the sector ABC to the sector EFG . Α E AA B C F D H 214. The ALTITUDE OF A TRIANGLE is the perpendicular , which measures the distance of any one of its vertices from the ...
... similar to the arc FG ; the segment BDC to the segment FHG , and the sector ABC to the sector EFG . Α E AA B C F D H 214. The ALTITUDE OF A TRIANGLE is the perpendicular , which measures the distance of any one of its vertices from the ...
Página 99
... similar . Let the two triangles ABC , DCE be equiangular ; the angle BAC being equal to the angle CDE , the angle A B C to the angle DCE , and the angle A CB to the angle DEC , then the homologous sides will be B proportional , and we ...
... similar . Let the two triangles ABC , DCE be equiangular ; the angle BAC being equal to the angle CDE , the angle A B C to the angle DCE , and the angle A CB to the angle DEC , then the homologous sides will be B proportional , and we ...
Página 100
... similar ; since the third angles will also be equal , and the two tri- angles be equiangular . 261. Scholium . In similar triangles , the homologous sides are opposite to the equal angles ; thus the angle A C B being equal to D E C ...
... similar ; since the third angles will also be equal , and the two tri- angles be equiangular . 261. Scholium . In similar triangles , the homologous sides are opposite to the equal angles ; thus the angle A C B being equal to D E C ...
Otras ediciones - Ver todas
Elements of Geometry: With Practical Applications to Mensuration Benjamin Greenleaf Vista completa - 1874 |
Elements of Geometry: With Practical Application to Mensuration Benjamin Greenleaf Vista completa - 1869 |
Elements of Geometry: With Practical Applications to Mensuration Benjamin Greenleaf Vista completa - 1872 |
Términos y frases comunes
A B C ABCD adjacent angles altitude angle ACB angle equal arc A B base bisect chord circle circumference circumscribed cone convex surface cosec Cosine Cotang cylinder diagonal diameter distance divided drawn equal Prop equilateral triangle equivalent exterior angle feet formed frustum gles greater half the sum hence homologous hypothenuse inches included angle inscribed isosceles less Let ABC line A B logarithmic sine measured by half multiplied number of sides parallel parallelogram parallelopipedon pendicular perimeter perpendicular polyedron prism PROBLEM PROPOSITION pyramid quadrantal radii radius ratio rectangle regular polygon right angles right-angled triangle rods Scholium secant segment side A B similar slant height solve the triangle sphere spherical polygon spherical triangle Tang tangent THEOREM triangle ABC triangle equal trigonometric functions vertex
Pasajes populares
Página 59 - 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 37 - 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 120 - At a point in a given straight line to make an angle equal to a given angle.
Página 52 - 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.
Página 19 - In an isosceles triangle, the angles opposite the equal sides are equal.
Página 199 - Any two rectangular parallelopipedons are to each other as the products of their bases by their altitudes ; that is to say, as the products of their three dimensions.
Página 121 - 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 103 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Página 2 - The logarithm of any POWER of a number is equal to the product of the logarithm of the number by the exponent of the power. For let m be any number, and take the equation (Art.
Página 2 - The logarithm of any power of a number is equal to the logarithm of the number multiplied by the exponent of the power.