Elements of Geometry and Trigonometry from the Works of A.M. Legendre: Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page ii
... SPHERICAL PROJEC TIONS . Babies ' Shades , Shadows , and Linzar Perspective . Davies ' Analytical Geometry - Embracing the EQUATIONS OF THE POINT AND STRAIGHT LINE - of the CONIC SECTIONS - of the LINE AND PLANE IN SPACE ; also , the ...
... SPHERICAL PROJEC TIONS . Babies ' Shades , Shadows , and Linzar Perspective . Davies ' Analytical Geometry - Embracing the EQUATIONS OF THE POINT AND STRAIGHT LINE - of the CONIC SECTIONS - of the LINE AND PLANE IN SPACE ; also , the ...
Page v
... 35 87 122 135 BOOK VI . Planes and Polyedral Angles ............ . 156 BOOK VII . Polyedrons , .... 174 BOOK VIII . The Three Round Bodies , ... 202 BOOK IX . Spherical Geometry , 227 Note A , .. The Regular Polyedrons ,. APPENDIX .
... 35 87 122 135 BOOK VI . Planes and Polyedral Angles ............ . 156 BOOK VII . Polyedrons , .... 174 BOOK VIII . The Three Round Bodies , ... 202 BOOK IX . Spherical Geometry , 227 Note A , .. The Regular Polyedrons ,. APPENDIX .
Page vii
... SPHERICAL TRIGONOMETRY . Spherical Triangle , Defined , ... Spherical Trigonometry , Defined ,. First Principles , .. Napier's Analogies , .. Napier's Circular Parts , - Theorems , Solution of Right - Angled Spherical Triangles , by ...
... SPHERICAL TRIGONOMETRY . Spherical Triangle , Defined , ... Spherical Trigonometry , Defined ,. First Principles , .. Napier's Analogies , .. Napier's Circular Parts , - Theorems , Solution of Right - Angled Spherical Triangles , by ...
Page viii
... Spherical Zone , .. 365 Solidity of a Sphere , .. 366 Solidity of a Spherical Segment ,. 366 Surface of a Spherical Triangle ,. 366 Surface of a Spherical Polygon , - 367 Of the Regular Polyedrons , .. 367 Theorem , ... 367 Method of ...
... Spherical Zone , .. 365 Solidity of a Sphere , .. 366 Solidity of a Spherical Segment ,. 366 Surface of a Spherical Triangle ,. 366 Surface of a Spherical Polygon , - 367 Of the Regular Polyedrons , .. 367 Theorem , ... 367 Method of ...
Page 204
... SPHERE is a solid terminated by a curved sur- face , all the points of which are equally distant from a point within , called the centre . The sphere may be gen- erated by the revolution of a semicircle DAE , about its diameter DE : for ...
... SPHERE is a solid terminated by a curved sur- face , all the points of which are equally distant from a point within , called the centre . The sphere may be gen- erated by the revolution of a semicircle DAE , about its diameter DE : for ...
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Common terms and phrases
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
Popular passages
Page 27 - If two triangles have two sides of the one equal to two sides of the...
Page 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Page 256 - The logarithm of . the quotient of two numbers, is equal to the logarithm of the dividend diminished by the logarithm of the divisor.
Page 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.
Page 26 - The sum of any two sides of a triangle is greater than the third side.
Page 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Page 93 - The area of a parallelogram is equal to the product of its base and altitude.
Page 358 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...
Page 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.
Page 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.