Elements of Geometry and Trigonometry Translated from the French of A.M. Legendre, by David Brewster: Revised and Adapted to the Course of Mathematical Instruction in the United States |
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Page 41
... centre . The circle is the space terminated by A this curved line . * 2. Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E H G eter ; every line which , like AB ...
... centre . The circle is the space terminated by A this curved line . * 2. Every straight line , CA , CE , CD , drawn from the centre to the circum- ference , is called a radius or semidiam- F E H G eter ; every line which , like AB ...
Page 42
... the A curve line AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
... the A curve line AFB , otherwise there would , in the one or the other , be points unequally dis- tant from the centre , which is contrary to the definition of a circle . PROPOSITION II . THEOREM . Every chord is less than 42 GEOMETRY .
Page 43
... centre ; and hence , there would be three equal straight lines drawn from the same point to the same straight line , which is impossible ( Book Î . Prop . XV . Cor . 2. ) . PROPOSITION IV . THEOREM . In the same circle , or in equal ...
... centre ; and hence , there would be three equal straight lines drawn from the same point to the same straight line , which is impossible ( Book Î . Prop . XV . Cor . 2. ) . PROPOSITION IV . THEOREM . In the same circle , or in equal ...
Page 45
... centre of the circle , and through the middle of the arc subtended by that chord . For , this perpendicular is the same as the one let fall from the centre on the same chord , since both of them pass through the centre and middle of the ...
... centre of the circle , and through the middle of the arc subtended by that chord . For , this perpendicular is the same as the one let fall from the centre on the same chord , since both of them pass through the centre and middle of the ...
Page 46
... centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we say farther , that ...
... centre O , with the radius OB , will pass through the three given points A , B , C. We have now shown that one circumference can always be made to pass through three given points , not in the same straight line : we say farther , that ...
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Common terms and phrases
adjacent adjacent angles altitude angle ACB angle BAC ar.-comp base multiplied bisect Book VII centre chord circ circumference circumscribed common cone convex surface Cosine Sine Cotang cylinder diagonal diameter dicular distance divided draw drawn equally distant equations equivalent feet figure find the area formed four right angles frustum given angle given line gles greater hence homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC logarithm number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular perpendicular let fall plane MN polyedron polygon ABCDE PROBLEM proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant segment similar slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex