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. ) . PROPOSITION XV . THEOREM . If from a point without a straight line , a perpendicular be let fall on the line , and obliqué lines be drawn to different points : 1st , The perpendicular will be ...
... whole , which is impossible ( Ax . 8. ) . PROPOSITION XV . THEOREM . If from a point without a straight line , a perpendicular be let fall on the line , and obliqué lines be drawn to different points : 1st , The perpendicular will be ...
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 centre chord circ circumference circumscribed common cone consequently convex surface cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equation equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed circle inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides opposite parallelogram parallelopipedon pendicular perimeter perpen perpendicular plane MN polyedron polygon ABCDE prism proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABC Scholium secant secant line segment side BC similar solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex