Elements of Geometry and Trigonometry |
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Page 27
... 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 + GOD is equal to two right ...
... 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 + GOD is equal to two right ...
Page 28
... parallel to a third line , are parallel to each other . Let CD and AB be parallel to the third line EF ; then are they parallel to each other . Draw PQR perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be ...
... parallel to a third line , are parallel to each other . Let CD and AB be parallel to the third line EF ; then are they parallel to each other . Draw PQR perpendicular to EF , and cutting AB , CD . Since AB is parallel to EF , PR will be ...
Page 29
... parallel and lying in the same di- rection , the two angles will be equal . Let BAC and DEF be the two angles , having AB parallel to ED , and AC to EF ; then will the angles be equal . For , produce DE , if necessary , till it meets AC ...
... parallel and lying in the same di- rection , the two angles will be equal . Let BAC and DEF be the two angles , having AB parallel to ED , and AC to EF ; then will the angles be equal . For , produce DE , if necessary , till it meets AC ...
Page 30
... parallel to BC , the part BAE is equal to the angle B , and the other part DAE is equal to the angle C. PROPOSITION XXVI . THEOREM . The sum of all the interior angles of a polygon , is equal to two right angles , taken as many times ...
... parallel to BC , the part BAE is equal to the angle B , and the other part DAE is equal to the angle C. PROPOSITION XXVI . THEOREM . The sum of all the interior angles of a polygon , is equal to two right angles , taken as many times ...
Page 32
... parallel , they have also the D angle ADB = DBC , ( Prop . XX . Cor . 2. ) ; and since AB , CD , are parallel , the angle ABD BDC : hence the two triangles are equal ( Prop . VI . ) ; therefore the side AB , opposite the an- gle ADB ...
... parallel , they have also the D angle ADB = DBC , ( Prop . XX . Cor . 2. ) ; and since AB , CD , are parallel , the angle ABD BDC : hence the two triangles are equal ( Prop . VI . ) ; therefore the side AB , opposite the an- gle ADB ...
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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