## Elements of Geometry and Trigonometry |

### From inside the book

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**Hence**, the angle FCD is equal to the angle FCE ( Ax . 10. ) ; which can only be the case when the lines CD and CE coincide : therefore , the straight lines which have two points A and B common , cannot separate at any point , when ... Page 17

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**Hence**, the point D , falling at the same time in the two straight lines BA and CA , must fall at their intersection A :**hence**, the two triangles EDF , BAC , coincide with each other , and are therefore equal ( Ax . 13. ) . D ' Cor ... Page 23

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**hence**the third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half of ABF , is shorter than AC , the half of ACF ;**hence**... Page 27

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**hence**we shall have two lines GB , GH , drawn through the same point G and parallel to CD , which is impossible ( Ax . 12. ) :**hence**, GB and GH should coincide , and OGB + GOD is equal to two right angles . In the same manner it may be ... Page 28

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**Hence**AB and CD are . perpendicular to the same straight line ;**hence**they are parallel ( Prop . XVIII . ) . R Q P F D B PROPOSITION XXIII . THEOREM . Two parallels are every where equally distant . Two parallels AB , CD , being C H ...### 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 equation 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 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-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