Elements of Geometry and Trigonometry |
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Page 16
If two triangles have two sides and the included angle of the one , equal to two sides and the included angle of the other , each to each , the two triangles will be equal . Let the side ED be equal to the side BA , the side DF to the ...
If two triangles have two sides and the included angle of the one , equal to two sides and the included angle of the other , each to each , the two triangles will be equal . Let the side ED be equal to the side BA , the side DF to the ...
Page 17
If two triangles have two angles and the included side of the one , equal to two angles and the included side of the other , each to each , the two triangles will be equal . D Let the angle E be equal to the angle B , the angle F to the ...
If two triangles have two angles and the included side of the one , equal to two angles and the included side of the other , each to each , the two triangles will be equal . D Let the angle E be equal to the angle B , the angle F to the ...
Page 18
If two triangles have two sides of the one equal to two sides of the other , each to each , and the included angles unequal , the third sides will be unequal ; and the greater side will belong to the triangle which has the greater ...
If two triangles have two sides of the one equal to two sides of the other , each to each , and the included angles unequal , the third sides will be unequal ; and the greater side will belong to the triangle which has the greater ...
Page 21
Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle ...
Now , in the two triangles BDC , BAC , we have BD - AC , by construction ; the angle B equal to the angle ACB , by hypothesis ; B and the side BC common : therefore , the two triangles , BDC , BAC , have two sides and the included angle ...
Page 32
Two parallels AB , CD , included between two other parallels AD , BC , are equal ; and the diagonal DB divides the parallelogram into two equal triangles . - D PROPOSITION XXIX . THEOREM . If the opposite sides of a quadrilateral are ...
Two parallels AB , CD , included between two other parallels AD , BC , are equal ; and the diagonal DB divides the parallelogram into two equal triangles . - D PROPOSITION XXIX . THEOREM . If the opposite sides of a quadrilateral are ...
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ABCD adjacent altitude base become Book called centre chord circle circumference circumscribed common cone consequently contained Cosine Cotang cylinder described determine diameter difference distance divided draw drawn equal equations equivalent expressed extremities faces feet figure follows formed four frustum give given gles greater half hence homologous hypothenuse included inscribed intersection less let fall logarithm manner means measured meet middle multiplied number of sides opposite parallel parallelogram pass perpendicular plane polygon prism PROBLEM Prop proportional PROPOSITION pyramid quadrant quantities radii radius ratio reason rectangle regular remaining right angles Scholium segment sides similar Sine solid solid angle sphere spherical triangle square straight line suppose taken Tang tangent THEOREM third triangle triangle ABC unit vertex whole