Elements of Geometry and Trigonometry |
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Page 14
The sum of all the successive angles , BAC , CAD , DAE , EAF , formed on the same side of the straight line BF , is equal to two right angles ; for their sum is equal to that of the two adjacent an- , gles , BAC , CAF .
The sum of all the successive angles , BAC , CAD , DAE , EAF , formed on the same side of the straight line BF , is equal to two right angles ; for their sum is equal to that of the two adjacent an- , gles , BAC , CAF .
Page 16
The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two ...
The four angles formed about a point by two straight lines , which intersect each other , are together equal to four right angles : for the sum of the two angles ACE , ECB , is equal to two right angles ; and the sum of the other two ...
Page 26
When two parallel straight lines AB , CD , are met by a 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 ...
When two parallel straight lines AB , CD , are met by a 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 ...
Page 27
We see that of the eight angles formed by a line cutting two parallel lines obliquely , the four acute angles are equal to each other , and so also are the four obtuse angles . PROPOSITION XXI . THEOREM . If a straight line meet two ...
We see that of the eight angles formed by a line cutting two parallel lines obliquely , the four acute angles are equal to each other , and so also are the four obtuse angles . PROPOSITION XXI . THEOREM . If a straight line meet two ...
Page 41
An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . * Note . In common language , the circle is sometimes confounded with its circumference : but the correct expression may ...
An inscribed angle is one which , like BAC , has its vertex in the circumference , and is formed by two chords . * Note . In common language , the circle is sometimes confounded with its circumference : but the correct expression may ...
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ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently construction contained corresponding cosine Cotang cylinder described diameter difference distance divided draw drawn equal equation equivalent evident expressed extremities fall figure follows formed formulas four frustum give given gles greater half hence homologous included inscribed intersection less likewise logarithm manner means measured meet middle multiplied opposite parallel parallelogram parallelopipedon pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment shown sides similar sine solid solid angle sphere spherical triangle square straight line Suppose surface taken tang tangent THEOREM third triangle triangle ABC vertex whole