Elements of Geometry and Trigonometry |
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Page 13
... whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right angles are equal to each other . 11 From one point to another only one straight line can be drawn . 12. Through the same point ...
... whole is greater than any of its parts . 9. The whole is equal to the sum of all its parts . 10. All right angles are equal to each other . 11 From one point to another only one straight line can be drawn . 12. Through the same point ...
Page 14
... whole extent , and form one and the same straight line . Let A and B be the two common points . In the first place it is evident that the two lines must coincide entirely between A and B , for otherwise there would be two straight lines ...
... whole extent , and form one and the same straight line . Let A and B be the two common points . In the first place it is evident that the two lines must coincide entirely between A and B , for otherwise there would be two straight lines ...
Page 21
... whole ( Ax . 8. ) ; hence , there is no inequality between the sides BA , AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle is opposite to the greater an gle ; and ...
... whole ( Ax . 8. ) ; hence , there is no inequality between the sides BA , AC ; therefore , the triangle BAC is isosceles . PROPOSITION XIII . THEOREM . The greater side of every triangle is opposite to the greater an gle ; and ...
Page 22
... whole , which is impossible ( Ax . 8. ) . A PROPOSITION XV . THEOREM . C B If from a point without a straight line , a perpendicular be let fall on the line , and oblique lines be drawn to different points : ยท 1st , The perpendicular ...
... whole , which is impossible ( Ax . 8. ) . A PROPOSITION XV . THEOREM . C B If from a point without a straight line , a perpendicular be let fall on the line , and oblique lines be drawn to different points : ยท 1st , The perpendicular ...
Page 34
... whole , and one of those parts being considered as an unit of measure , the magnitude may be expressed by the number of units it contains . If the other magnitude contain a certain number of those units , it also may be expressed by the ...
... whole , and one of those parts being considered as an unit of measure , the magnitude may be expressed by the number of units it contains . If the other magnitude contain a certain number of those units , it also may be expressed by the ...
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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 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 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-ABCDE Scholium secant segment similar Sine Cotang slant height solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex