## Elements of Geometry and Trigonometry |

### From inside the book

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**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 may be shown that the ... Page 21

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**follows**, from what has just been proved , that AB AC ; which is contrary to the hypothesis . If the angle C - B , then the side AB = AC ( Prop . XII . ) ; which is also contrary to the supposition . Therefore , when AB > AC , the angle ... Page 32

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**follows**that the angle A is equal to the angle C ; and also that the angle ADC com- posed of the two ADB , BDC , is equal to ABC , composed of the two equal angles DBC , ABD : hence the opposite angles of a parallelogram are also equal ... Page 33

... therefore equal : whence it

... therefore equal : whence it

**follows**that the angles AEB , BEC , are equal , and therefore , that the two diagonals of a rhombus cut each other at right angles . } BOOK II . OF RATIOS AND PROPORTIONS . Definitions 5 BOOK I. 33. Page 34

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**follows**, that magnitudes may be rep- resented by numbers to any degree of exactness , or they will differ from their numerical representatives by less than any assignable quantity . Therefore , of two magnitudes , A and B , we may ...### 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