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 páginas |
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Página 10
... line itself : hence , a point has neither length , breadth , nor thickness , but place or position only . 7. Although we use the term solid to denote a given portion of space , the term surface to denote the boundary of a solid , the term ...
... line itself : hence , a point has neither length , breadth , nor thickness , but place or position only . 7. Although we use the term solid to denote a given portion of space , the term surface to denote the boundary of a solid , the term ...
Página 20
... line is the shortest distance between two points . 13. Through the same point , only one straight line can be drawn which shall be parallel to a given line . 14. Magnitudes , which being applied the one to the other , coincide ...
... line is the shortest distance between two points . 13. Through the same point , only one straight line can be drawn which shall be parallel to a given line . 14. Magnitudes , which being applied the one to the other , coincide ...
Página 31
... given point , without a straight line , only one perpen- dicular can be drawn to that line . A D- -E B F Let A be the point , and DE the given line . Let us suppose that we can draw two perpendiculars , AB , AC . Pro- long either of ...
... given point , without a straight line , only one perpen- dicular can be drawn to that line . A D- -E B F Let A be the point , and DE the given line . Let us suppose that we can draw two perpendiculars , AB , AC . Pro- long either of ...
Página 32
... line . Cor . At a given point C , in the line AB , it is also impossible to erect more than one perpendicular to that line . For , if CD , CE , were both perpendicular to AB , the angles A- BCD , BCE , would both be right E D V -B ...
... line . Cor . At a given point C , in the line AB , it is also impossible to erect more than one perpendicular to that line . For , if CD , CE , were both perpendicular to AB , the angles A- BCD , BCE , would both be right E D V -B ...
Página 33
... lines , which meet the given line at equal distances from the perpendicular , are equal . Thirdly . Since the point C is within the triangle FDA , the sum of the sides FD , DA , is greater than the sum of the lines FC , CA ( P. 8 ) ...
... lines , which meet the given line at equal distances from the perpendicular , are equal . Thirdly . Since the point C is within the triangle FDA , the sum of the sides FD , DA , is greater than the sum of the lines FC , CA ( P. 8 ) ...
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Términos y frases comunes
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
Pasajes populares
Página 27 - If two triangles have two sides of the one equal to two sides of the...
Página 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Página 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Página 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.
Página 26 - The sum of any two sides of a triangle is greater than the third side.
Página 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Página 93 - The area of a parallelogram is equal to the product of its base and altitude.
Página 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Página 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.
Página 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.