The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 18
... THEOR . 099 .. IF two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . • " Let ABC be a triangle having the angle THE ELEMENTS.
... THEOR . 099 .. IF two angles of a triangle be equal to one another , the sides also which subtend , or are opposite to , the equal angles , shall be equal to one another . • " Let ABC be a triangle having the angle THE ELEMENTS.
Página 19
... THEOR . B b 4. 1 . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base See Note . equal to one another , and likewise those which are ...
... THEOR . B b 4. 1 . C UPON the same base , and on the same side of it , there cannot be two triangles that have their sides which are terminated in one extremity of the base See Note . equal to one another , and likewise those which are ...
Página 26
... THEOR . IF one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of ...
... THEOR . IF one side of a triangle be produced , the exterior angle is greater than either of the interior opposite angles . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is greater than either of ...
Página 27
... THEOR . 2.9 THE greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC , is also greater than the angle BCA . Because AC is greater than ...
... THEOR . 2.9 THE greater side of every triangle is opposite to the greater angle . Let ABC be a triangle , of which the side AC is greater than the side AB ; the angle ABC , is also greater than the angle BCA . Because AC is greater than ...
Página 28
... THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC ...
... THEOR . ANY two sides of a triangle are together greater than the third side . Let ABC be a triangle ' ; any two sides of it together are greater than the third side , viz . the sides BA , AC greater than the side BC ; and AB , BC ...
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altitude angle ABC angle BAC base BC BC is equal BC is given bisected Book XI centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition pyramid Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar solid angle solid parallelopiped square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore