## Elements of Geometry and Trigonometry |

### From inside the book

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**theorem**, or the solution of a problem . The common name , proposition , is applied indifferently , to**theorems**, problems , and lemmas . A corollary is an obvious consequence , deduced from one or several propositions . A scholium is a ... Page 14

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**THEOREM**. Two straight lines , which have two points common , coincide with each other throughout their 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 ... Page 15

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**THEOREM**. If a straight line meet two other straight lines at a common point , making the sum of the two adjacent angles equal to two right angles , the two straight lines which are met , will form one and the same straight line . Let ... Page 18

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**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 the shortest dis ... Page 19

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**theorem**, AG + GC < AB + BC ; and , taking AG from the one , and its equal AB from the other , there will remain GC < BC or BC > EF . B Scholium . Conversely , if two sides BA , AC , of the triangle BAC , are equal to the two ED , DF ...### 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 convex surface Cosine Cotang cylinder diagonal diameter dicular distance draw drawn equal angles equally distant equiangular equivalent figure formed four right angles frustum given angle given line gles greater homologous sides hypothenuse inscribed polygon intersection less Let ABC let fall logarithm measured by half number of sides oblique lines 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 sine solid angle solid described sphere spherical polygon spherical triangle square described straight line tang tangent THEOREM triangle ABC triangular prism vertex