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 viii
... Adjacent Faces of a Regular Polyedron , .. 368 Table of Regular Polyedrons whose Edges are 1 , ......... . 369 Solidity of a Regular Polyedron , ... 369 ELEMENTS OF GEOMETRY . INTRODUCTION . 1. SPACE extends indefinitely viii CONTENTS .
... Adjacent Faces of a Regular Polyedron , .. 368 Table of Regular Polyedrons whose Edges are 1 , ......... . 369 Solidity of a Regular Polyedron , ... 369 ELEMENTS OF GEOMETRY . INTRODUCTION . 1. SPACE extends indefinitely viii CONTENTS .
Σελίδα 156
... edge of the angle . A diedral angle is measured by the angle contained be- tween two lines , one drawn in each face , and both perpen- dicular to the common intersection at the same point . This angle may be acute , obtuse , or a right ...
... edge of the angle . A diedral angle is measured by the angle contained be- tween two lines , one drawn in each face , and both perpen- dicular to the common intersection at the same point . This angle may be acute , obtuse , or a right ...
Σελίδα 170
... edges in the points A , B , C , D , E , and the faces in the lines AB , BC , CD , DE , EA . From any point of this plane , as O , draw the straight lines OA , OB , OC , OD , OE . S E D A B We thus form two sets of triangles , one set ...
... edges in the points A , B , C , D , E , and the faces in the lines AB , BC , CD , DE , EA . From any point of this plane , as O , draw the straight lines OA , OB , OC , OD , OE . S E D A B We thus form two sets of triangles , one set ...
Σελίδα 174
... edges , formed by the intersection of the lateral faces , are perpendicular to the planes of the bases . Each edge is then equal to the altitude of the prism . In every other case , the prism is oblique , and each edge is then greater ...
... edges , formed by the intersection of the lateral faces , are perpendicular to the planes of the bases . Each edge is then equal to the altitude of the prism . In every other case , the prism is oblique , and each edge is then greater ...
Σελίδα 176
... edges , or angles , are called homologous . 18. A regular polyedron is one whose faces are equal and regular polygons , and whose polyedral angles are equal . PROPOSITION I. THEOREM . The convex surface of a right prism is equal to the ...
... edges , or angles , are called homologous . 18. A regular polyedron is one whose faces are equal and regular polygons , and whose polyedral angles are equal . PROPOSITION I. THEOREM . The convex surface of a right prism is equal to 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.