## Elements of Geometry and Trigonometry |

### From inside the book

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**PROPOSITION**VII . THEOREM . The sum of any two sides of a triangle , is greater than the third side . 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 ... Page 19

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**proposition**, according as the point G falls without the triangle ABC , or upon its base BC , or within it . First Case . The straight line GC < GI + IC , and the straight line AB < AI + IB ; therefore , GC + AB < GI + AI + IC + IB , or ... Page 20

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**proposition**, that the side EF must be greater than BC ; and if the angle D were less than A , it would follow , that the side EF must be less than BC : but EF is equal to BC , by hypothesis ; therefore , the angle D can neither be ... Page 21

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**PROPOSITION**XII . THEOREM . Conversely , if two angles of a triangle are equal , the sides oppo- site them are also equal , and the triangle is isosceles . Let the angle ABC be equal to the angle ACB ; then will the side AC be equal to ... Page 22

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**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 shorter than any oblique line . 2d , Any two ...### 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