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 58
... TANGENT is a line which has but one point in common with the cir cumference . Ө The point where the tangent touches the circumference , is called the point of contact . 10. Two circumferences touch each other when they have but one ...
... TANGENT is a line which has but one point in common with the cir cumference . Ө The point where the tangent touches the circumference , is called the point of contact . 10. Two circumferences touch each other when they have but one ...
Σελίδα 64
... tangent to the circumference . Let the line BD be perpendicular to the radius CA at its extremity A ; then will it be tangent to the circumfer- ence . A E D Ο For , every oblique line CE 64 GEOMETRY .
... tangent to the circumference . Let the line BD be perpendicular to the radius CA at its extremity A ; then will it be tangent to the circumfer- ence . A E D Ο For , every oblique line CE 64 GEOMETRY .
Σελίδα 65
... tangent ( D. 9 ) . Cor . 1. Conversely , if a straight line be tangent to a circle , it will be perpendicular to the radius drawn to the point of contact . Let BAD be a tangent , and CA a radius drawn through the point of contact A ...
... tangent ( D. 9 ) . Cor . 1. Conversely , if a straight line be tangent to a circle , it will be perpendicular to the radius drawn to the point of contact . Let BAD be a tangent , and CA a radius drawn through the point of contact A ...
Σελίδα 66
... tangent , draw the radius CH to the point of contact H ; it will be perpendicular to the tan- gent DE ( P. 9 , c . 1 ) , and also to its parallel MP ( B. I. , P. 20 , c . 1 ) . But since CH is perpendicular to the chord MP , the point H ...
... tangent , draw the radius CH to the point of contact H ; it will be perpendicular to the tan- gent DE ( P. 9 , c . 1 ) , and also to its parallel MP ( B. I. , P. 20 , c . 1 ) . But since CH is perpendicular to the chord MP , the point H ...
Σελίδα 69
... tangent to each other at the point A. For , they have only the point A common , and if through A , AE be drawn perpendicular to AD , it will be a common tangent to all the circles . Scholium . 2. Two circumferences must occupy with res ...
... tangent to each other at the point A. For , they have only the point A common , and if through A , AE be drawn perpendicular to AD , it will be a common tangent to all the circles . Scholium . 2. Two circumferences must occupy with res ...
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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.