## Elements of Geometry and Trigonometry |

### From inside the book

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**Let ABC**be a triangle : then will the sum of two of its sides , as AC , CB , be greater than the third side AB . For , the line AB is the shortest dis- tance between the points A and B ( Def . 3. ) ; hence AC + CB is greater than AB . B ... Page 19

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**ABC**, or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB ...**Let**the side ED = BA , the BOOK I. 19. Page 21

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**Let**the angle**ABC**be equal to the angle ACB ; then will the side AC be equal to the side AB . D For , if these sides are not equal , suppose AB to be the greater . Then , take BD equal to AC , and draw CD . Now , in the two triangles ... Page 29

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**Let ABC**be any triangle : then will the an- gle C + A + B be equal to two right angles . E A. D For , produce the side CA towards D , and at the point A , draw AE parallel to BC . Then , since AE , CB , are parallel , and CAD cuts them ... Page 30

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**ABC**, the exterior angle BAD is equal to the sum of the two interior opposite angles B and C. For , AE being ...**Let**ABCDEFG be the proposed polygon . If from the vertex of any one angle A , diagonals B AC , AD , AE , AF , be drawn ...### Other editions - View all

### 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