Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United StatesA.S. Barnes & Company, 1854 - 432 σελίδες |
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Σελίδα 16
... opposite the right angle is called the hypothenuse , and the other two sides , the base and perpen- dicular . 6. An obtuse - angled triangle is one which has an obtuse angle . 24. There are three kinds of QUADRILATERALS : 1. The ...
... opposite the right angle is called the hypothenuse , and the other two sides , the base and perpen- dicular . 6. An obtuse - angled triangle is one which has an obtuse angle . 24. There are three kinds of QUADRILATERALS : 1. The ...
Σελίδα 23
... opposite or vertical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting each other at C ; then will the angle ECB be equal to the angle ACD , and the angle ACE to the angle DCB . For , since the ...
... opposite or vertical angles , which they form , are equal . Let AB and DE be two straight lines , intersecting each other at C ; then will the angle ECB be equal to the angle ACD , and the angle ACE to the angle DCB . For , since the ...
Σελίδα 29
... opposite the equal sides , and consequently , the equal sides opposite the equal angles : thus , the equal angles D and A , lie opposite the equal sides EF and BC . PROPOSITION XI . THEOREM . In an isosceles triangle , the angles opposite ...
... opposite the equal sides , and consequently , the equal sides opposite the equal angles : thus , the equal angles D and A , lie opposite the equal sides EF and BC . PROPOSITION XI . THEOREM . In an isosceles triangle , the angles opposite ...
Σελίδα 30
... opposite angle . In an isosceles triangle , however , that side is generally assumed as the base , which is not equal to either of the other two . PROPOSITION XII . THEOREM . Conversely : If two angles of a triangle are equal , the ...
... opposite angle . In an isosceles triangle , however , that side is generally assumed as the base , which is not equal to either of the other two . PROPOSITION XII . THEOREM . Conversely : If two angles of a triangle are equal , the ...
Σελίδα 31
... opposite to AB , be greater than the angle B , opposite to AC . For , if the angle C < B , it follows , from what has just been proved , that AB < AC ; which is contrary to the hypothesis . If the angle C - B , then the side AB = AC ( P ...
... opposite to AB , be greater than the angle B , opposite to AC . For , if the angle C < B , it follows , from what has just been proved , that AB < AC ; which is contrary to the hypothesis . If the angle C - B , then the side AB = AC ( P ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
adjacent angles altitude angle ACB angle BAD base ABCD bisect centre chord circ circumference circumscribed common comp cone consequently convex surface cosine Cotang cylinder diagonal diameter distance divided draw drawn edges equations equivalent feet figure find the area frustum given angle given line given point gles greater hence homologous homologous sides hypothenuse included angle inscribed circle intersect less Let ABC let fall logarithm magnitudes measured by half middle point number of sides oblique lines opposite parallelogram parallelopipedon pendicular perimeter perpendicular plane MN polyedral angle polyedron PROBLEM PROPOSITION pyramid quadrant radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium secant segment side BC similar sine slant height solidity sphere spherical polygon spherical triangle square described straight line Tang tangent THEOREM triangle ABC triangular prism triedral angles vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 27 - If two triangles have two sides of the one equal to two sides of the...
Σελίδα 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Σελίδα 97 - The square described on the hypothenuse of a right-angled triangle is equivalent to the sum of the squares described on the other two sides.
Σελίδα 26 - The sum of any two sides of a triangle is greater than the third side.
Σελίδα 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Σελίδα 93 - The area of a parallelogram is equal to the product of its base and altitude.
Σελίδα 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Σελίδα 323 - A'B'C', and applying the law of cosines, we have cos a' = cos b' cos c' + sin b' sin c' cos A'. Remembering the relations a' = 180° -A, b' = 180° - B, etc. (this expression becomes cos A = — cos B cos C + sin B sin C cos a.
Σελίδα 64 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.