Elements of Geometry and Trigonometry |
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Page 24
... perpendicular is equally distant from the extremities A and B. E B Secondly , Let I be a point out of the perpen- dicular . If IA and IB be drawn , one of these lines will cut the perpendicular in D ; from which , drawing DB , we shall ...
... perpendicular is equally distant from the extremities A and B. E B Secondly , Let I be a point out of the perpen- dicular . If IA and IB be drawn , one of these lines will cut the perpendicular in D ; from which , drawing DB , we shall ...
Page 25
... perpendicular to AB ; then will they be parallel . For , if they could meet in a point Q , on either side of AB ... perpendicular to EC . It will also be perpendicular to BD . For , the sum BAC + ABD is equal to two right angles , by ...
... perpendicular to AB ; then will they be parallel . For , if they could meet in a point Q , on either side of AB ... perpendicular to EC . It will also be perpendicular to BD . For , the sum BAC + ABD is equal to two right angles , by ...
Page 27
... perpendicular to one of two parallels , is perpendicular to the other . Cor . 2. If a straight line meet two parallel lines , the alternate angles will be equal . Let AB , CD , be the parallels , and FE the secant line . The sum OGB + ...
... perpendicular to one of two parallels , is perpendicular to the other . Cor . 2. If a straight line meet two parallel lines , the alternate angles will be equal . Let AB , CD , be the parallels , and FE the secant line . The sum OGB + ...
Page 28
... perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be perpendicular to AB ( Prop.E XX . Cor . 1. ) ; and since CD is parallel to EF , PR will for a like reason be perpen - C dicular to CD . Hence AB and CD ...
... perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be perpendicular to AB ( Prop.E XX . Cor . 1. ) ; and since CD is parallel to EF , PR will for a like reason be perpen - C dicular to CD . Hence AB and CD ...
Page 45
... perpendicular erected from the mid- A H dle of AB ; hence every point of this perpendicular must be equally distant from its two extremities A and B ( Book I. Prop . XVI . ) . Now , G is one of these points ; therefore AG , BG , are ...
... perpendicular erected from the mid- A H dle of AB ; hence every point of this perpendicular must be equally distant from its two extremities A and B ( Book I. Prop . XVI . ) . Now , G is one of these points ; therefore AG , BG , are ...
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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