Elements of Geometry: With Practical Applications to MensurationLeach, Shewell and Sanborn, 1863 - 320 páginas |
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Página 23
... ( Prop . IX . ) , the side OC in the triangle CDO is less than the sum of OD and D C. To each of these inequalities add B O , and we have the sum of BO and O C less than the sum of BO , OD , and DC ( Art . 34 , Ax . 4 ) ; or the sum of BO ...
... ( Prop . IX . ) , the side OC in the triangle CDO is less than the sum of OD and D C. To each of these inequalities add B O , and we have the sum of BO and O C less than the sum of BO , OD , and DC ( Art . 34 , Ax . 4 ) ; or the sum of BO ...
Página 25
... ( Prop . V. ) , and the side A E is equal to the side A C ( Prop . V. Cor . ) . Hence the two oblique lines , meeting the given line at equal distances from the perpendicular , are equal . Thirdly . The point C being in the triangle ADF ...
... ( Prop . V. ) , and the side A E is equal to the side A C ( Prop . V. Cor . ) . Hence the two oblique lines , meeting the given line at equal distances from the perpendicular , are equal . Thirdly . The point C being in the triangle ADF ...
Página 27
... ( Prop . XIV . Cor . 3 ) ; therefore its extremity , F , must fall below the line EG . The two tri- angles , A B C and ... ( Prop . V. Cor . ) . In the triangle DFG , since D G is equal to DF , the angle D F G is equal to the angle D G F ...
... ( Prop . XIV . Cor . 3 ) ; therefore its extremity , F , must fall below the line EG . The two tri- angles , A B C and ... ( Prop . V. Cor . ) . In the triangle DFG , since D G is equal to DF , the angle D F G is equal to the angle D G F ...
Página 28
... ( Prop . V. Cor . ) , which is contrary to the hypothesis ; neither can it be less , for then the side B C would be less than EF ( Prop . XVI . ) , which also is contrary to the hypothesis ; there- fore the angle A is not less than the ...
... ( Prop . V. Cor . ) , which is contrary to the hypothesis ; neither can it be less , for then the side B C would be less than EF ( Prop . XVI . ) , which also is contrary to the hypothesis ; there- fore the angle A is not less than the ...
Página 29
... ( Prop . XVI . ) ; and if the angle A were less than D , it would follow that the side BC would be less than EF . But by hypothesis BC is equal to EF ; hence the angle A can neither be greater nor less than D ; therefore it must be equal ...
... ( Prop . XVI . ) ; and if the angle A were less than D , it would follow that the side BC would be less than EF . But by hypothesis BC is equal to EF ; hence the angle A can neither be greater nor less than D ; therefore it must be equal ...
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.