## Elements of Geometry and Trigonometry |

### From inside the book

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**less**than any assignable quantity , has been taken from the Edinburgh Encyclopedia . It is proved in the corollaries that a polygon of an infinite number of sides becomes a circle , and this principle is made the basis of several ... Page 10

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**less**as the lines are more or**less**inclined or opened . The point of intersection A is the vertex of the angle , and the lines AB , AC , are its sides . A -B The angle is sometimes designated simply by the letter at the vertex A ... Page 18

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**less**than the sum of the two other sides of the triangle . Let any point , as O , be taken within the trian- gle BAC , and let the lines OB , OC , be drawn to the extremities of either side , as BC ; then will OB + OC < BA + AC . Let BO ... Page 19

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**less**than it . In the first case , the side BC would be equal to EF , ( Prop . V. Cor . ) ; in the second , CB would be**less**than EF ; but either of these results contradicts the hypothesis : therefore , BAC is greater than EDF ... Page 20

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**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_greater nor**less**than A ; therefore it must be equal to it . In the same manner it ...### Other editions - View all

### 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