Elements of Geometry and Trigonometry |
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Page 23
... third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half of ABF , is shorter than AC , the half of ACF ; hence , the ...
... third sides , CF and CA are equal ( Prop . V. Cor . ) . But ABF , being a straight line , is shorter than ACF , which is a broken line ( Def . 3. ) ; therefore , AB , the half of ABF , is shorter than AC , the half of ACF ; hence , the ...
Page 25
... third line , they will be parallel to each other : in other words , they will never meet , how far soever either way ... third line , making the sum of the interior angles on the same side of the line met , equal to two right angles ...
... third line , they will be parallel to each other : in other words , they will never meet , how far soever either way ... third line , making the sum of the interior angles on the same side of the line met , equal to two right angles ...
Page 26
... third line FE , the angles which are formed take particular names . Interior angles on the same side , are those which lie within the parallels , and on the same side of the secant line : thus , OGB , GOD , are interior angles on the ...
... third line FE , the angles which are formed take particular names . Interior angles on the same side , are those which lie within the parallels , and on the same side of the secant line : thus , OGB , GOD , are interior angles on the ...
Page 28
... 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 perpendicular ...
... 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 perpendicular ...
Page 29
... right angles ( Prop . I. ) . Cor . 1. Two angles of a triangle being given , or merely their sum , the third will be found by subtracting that sum from two right angles . C✶ Cor . 2. If two angles of one triangle are BOOK I. 29.
... right angles ( Prop . I. ) . Cor . 1. Two angles of a triangle being given , or merely their sum , the third will be found by subtracting that sum from two right angles . C✶ Cor . 2. If two angles of one triangle are BOOK I. 29.
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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