Elements of Geometry and Trigonometry |
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Page 43
... extremities . We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the ...
... extremities . We shall then have AD AC + CD ( Book I. Prop . VII . * ) ; A or AD < AB . Cor . Hence the greatest line which can be inscribed in a circle is its diameter . PROPOSITION III . THEOREM . A straight line cannot meet the ...
Page 45
... extremities A and B ( Book I. Prop . XVI . ) . Now , G is one of these points ; therefore AG , BG , are equal . But if the chord AG is equal to the chord GB , the arc AG will be equal to the arc GB ( Prop . IV . ) ; hence , the radius ...
... extremities A and B ( Book I. Prop . XVI . ) . Now , G is one of these points ; therefore AG , BG , are equal . But if the chord AG is equal to the chord GB , the arc AG will be equal to the arc GB ( Prop . IV . ) ; hence , the radius ...
Page 47
... extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe - r rence . For , every oblique line CE , is longer than the perpendicular CA ...
... extremity , is a tangent to the circumference . Let BD be perpendicular to the B radius CA , at its extremity A ; then will it be tangent to the circumfe - r rence . For , every oblique line CE , is longer than the perpendicular CA ...
Page 57
... extremities A and B , must both lie in the perpendicular raised from the middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line DE must itself be that perpendicular ...
... extremities A and B , must both lie in the perpendicular raised from the middle of AB ( Book I. Prop . XVI . Cor . ) . But only one straight line can pass through two given points ; hence the line DE must itself be that perpendicular ...
Page 59
... extremities A and B of the chord AB ; hence the line CD bi- sects the chord at right angles ( Book I. Prop . XVI . Cor . ) ; hence , it bisects the arc AB in the point E ( Prop . VI . ) . Secondly . Let it be required to divide the ...
... extremities A and B of the chord AB ; hence the line CD bi- sects the chord at right angles ( Book I. Prop . XVI . Cor . ) ; hence , it bisects the arc AB in the point E ( Prop . VI . ) . Secondly . Let it be required to divide the ...
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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 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