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 11
... which the mind acts and reasons : A but is , as it were , the word or sign which stands for and expresses the abstract idea . These considerations have induced me to represent the geometrical magnitudes INTRODUCTION . 11.
... which the mind acts and reasons : A but is , as it were , the word or sign which stands for and expresses the abstract idea . These considerations have induced me to represent the geometrical magnitudes INTRODUCTION . 11.
Σελίδα 39
... reason be E- R -D Q -B P perpendicular to CD . Hence , AB and CD are perpendicular to the same straight line ; hence , they are parallel ( P. 18 ) . PROPOSITION XXIII . THEOREM . Two parallels are everywhere equally distant . suppose FH ...
... reason be E- R -D Q -B P perpendicular to CD . Hence , AB and CD are perpendicular to the same straight line ; hence , they are parallel ( P. 18 ) . PROPOSITION XXIII . THEOREM . Two parallels are everywhere equally distant . suppose FH ...
Σελίδα 45
... reason AB is parallel to CD : therefore , the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the other sides are equal and parallel , and the figure ...
... reason AB is parallel to CD : therefore , the quadrilateral ABCD is a parallelogram . PROPOSITION XXX . THEOREM . If two opposite sides of a quadrilateral are equal and parallel , the other sides are equal and parallel , and the figure ...
Σελίδα 63
... reason ; therefore , it would be in both the lines DE , FG . But two straight lines cannot cut each other in more than one point ; hence , there is but one circumference which can pass through three given points . Cor . Two ...
... reason ; therefore , it would be in both the lines DE , FG . But two straight lines cannot cut each other in more than one point ; hence , there is but one circumference which can pass through three given points . Cor . Two ...
Σελίδα 72
... reasons . At all events , if the measurement of angles by the arcs of a circle is in any degree indirect , it is still very easy to obtain the direct and absolute measure by this method ; since , by comparing the fourth part of the ...
... reasons . At all events , if the measurement of angles by the arcs of a circle is in any degree indirect , it is still very easy to obtain the direct and absolute measure by this method ; since , by comparing the fourth part of the ...
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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.