Elements of Geometry and Trigonometry: With Applications in Mensuration |
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Page 23
... VIII . If two triangles have the three sides of the one equal to the three sides of the other , each to each , the three angles will also be equal , each to each . Let the two triangles ABC , ABD , have the side AB equal to the side AB ...
... VIII . If two triangles have the three sides of the one equal to the three sides of the other , each to each , the three angles will also be equal , each to each . Let the two triangles ABC , ABD , have the side AB equal to the side AB ...
Page 31
... viii ) . If the sides are unequal , suppose BC to be the greater , and take a part , BG , equal to EF , and draw AG . Then , in the two triangles ABG and DEF , the angle B is equal to the angle E , the side AB to the side DE , and the ...
... viii ) . If the sides are unequal , suppose BC to be the greater , and take a part , BG , equal to EF , and draw AG . Then , in the two triangles ABG and DEF , the angle B is equal to the angle E , the side AB to the side DE , and the ...
Page 32
... viii ) . THEOREM XX . The sum of the four angles of every quadrilateral is equal to four right angles . Let A CBD be a quadrilateral : then will A + B + C + D = four right angles . Let the diagonal DC be drawn dividing the quadrilateral ...
... viii ) . THEOREM XX . The sum of the four angles of every quadrilateral is equal to four right angles . Let A CBD be a quadrilateral : then will A + B + C + D = four right angles . Let the diagonal DC be drawn dividing the quadrilateral ...
Page 36
... viii ) ; hence , the angle ADB , opposite the side AB , is equal to the angle DBC opposite the side DC ; therefore , the sides AD , BC , are parallel ( Th . xiii ) . For a like reason DC is parallel to AB , and the figure ABCD is a ...
... viii ) ; hence , the angle ADB , opposite the side AB , is equal to the angle DBC opposite the side DC ; therefore , the sides AD , BC , are parallel ( Th . xiii ) . For a like reason DC is parallel to AB , and the figure ABCD is a ...
Page 42
... viii ) : that is , the angle CDA equal to CDB , and the angle ACD equal to the angle DCB . But , since the angle CDA is equal E to the angle CDB , the radius CE is perpendicular to the chord AB ( Bk . I. Def . 20 ) . Secondly . Since ...
... viii ) : that is , the angle CDA equal to CDB , and the angle ACD equal to the angle DCB . But , since the angle CDA is equal E to the angle CDB , the radius CE is perpendicular to the chord AB ( Bk . I. Def . 20 ) . Secondly . Since ...
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Common terms and phrases
adjacent angles allel altitude angles equal bisect called centre chains chord circle whose diameter circumference column common comp cone consequently convex surface Cosine Cosine D Cotang cylinder Davies decimal diagonal dicular distance divided draw equal Bk equal to half equivalent figure find the area frustum greater half the arc half the product hence horizontal hypothenuse inches included angle inscribed intersection Let ABCD logarithm lower base M.
M. Sine measured by half Mensuration of Surfaces number of sides opposite angles outward angle parallel parallelogram parallelopipedon pendicular pentagonal pyramid perimeter perpen perpendicular plane prism PROBLEM proportion pyramid quadrilateral radii radius ratio rectangle regular polygon Required the area rhombus right angled triangle right angles Bk segment side AC similar similar triangles slant height solidity sphere straight line suppose Tang tangent THEOREM triangle ABC upper base yards