Elements of Geometry and Trigonometry |
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Page 26
... Opposite exterior and interior angles lie on the same side of the secant line , the one without and the other within the parallels , but not adjacent : thus , EGB , GOD , are opposite exterior and interior angles ; and so also , are the ...
... Opposite exterior and interior angles lie on the same side of the secant line , the one without and the other within the parallels , but not adjacent : thus , EGB , GOD , are opposite exterior and interior angles ; and so also , are the ...
Page 29
... opposite one ACB ( Prop . XX . Cor . 3. ) ; in like manner , since AE , CB , are parallel , and AB cuts them , the alternate angles ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the three ...
... opposite one ACB ( Prop . XX . Cor . 3. ) ; in like manner , since AE , CB , are parallel , and AB cuts them , the alternate angles ABC , BAE , will be equal : hence the three angles of the triangle ABC make up the same sum as the three ...
Page 30
... opposite angles B and C. For , AE being 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 ...
... opposite angles B and C. For , AE being 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 ...
Page 32
... opposite the an- gle ADB , is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the op- posite sides of a parallelogram are equal . Again , since the triangles are equal , it follows ...
... opposite the an- gle ADB , is equal to the side DC , opposite the equal angle DBC ; and the third sides AD , BC , are equal : hence the op- posite sides of a parallelogram are equal . Again , since the triangles are equal , it follows ...
Page 33
... opposite the side AB , is equal to DBC , opposite CD ( Prop . X. ) ; therefore , the side AD is parallel to BC ( Prop . XIX . Cor . 1. ) . For a like reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram ...
... opposite the side AB , is equal to DBC , opposite CD ( Prop . X. ) ; therefore , the side AD is parallel to BC ( Prop . XIX . Cor . 1. ) . For a like reason AB is parallel to CD therefore the quadrilateral ABCD is a parallelogram ...
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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