## Elements of Geometry and Trigonometry |

### From inside the book

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**remaining**three are also respectively equal , namely , the side EF = BC , the angle E = B , and the angle F = C PROPOSITION VI . THEOREM . If two triangles have two angles and the included side of the one , equal to two angles and the ... Page 24

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**remaining**parts will also be equal , each to each , and the triangles themselves will be equal . A In the two right angled triangles BAC , EDF , let the hypothenuse AC = DF , and the side BA = ED ; then will the side BC = EF , the angle ... Page 33

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**remaining**sides will also be equal and parallel , and the figure will be a parallelogram . Let ABCD be a quadrilateral , having the sides AB , CD , equal and parallel ; then will the figure be a parallelogram . D C B For , draw the ... Page 37

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**remaining**terms will be propor- tional . PROPOSITION V. THEOREM . If two quantities be in proportion , they will be in proportion when Let taken inversely . M : N :: P : Q ; then will N : M :: Q : P . For , from the first proportion we ... Page 60

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**remaining**angle HEF will be the third angle required ; be- D cause those three angles are E T together equal to two right angles ( Book I. Prop . I. and XXV ) . PROBLEM VIII . Two sides of a triangle , and the angle which they contain ...### 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 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 produced proportional PROPOSITION pyramid quadrant quadrilateral quantities radii radius ratio rectangle regular polygon right angled triangle S-ABCDE 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