The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 12
... opposite sides equal to one another , but all its sides are not equal , nor its angles right angles . XXXIV . All other four sided figures besides these , 12 THE ELEMENTS An acute-angled triangle, is that which has ...
... opposite sides equal to one another , but all its sides are not equal , nor its angles right angles . XXXIV . All other four sided figures besides these , 12 THE ELEMENTS An acute-angled triangle, is that which has ...
Página 16
... equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; A 16 THE ELEMENTS.
... equal , each to each , viz . those to which the equal sides are opposite . Let ABC , DEF be two triangles which have the two sides AB , AC equal to the two sides DE , DF , each to each , viz . AB to DE , and AC to DF ; A 16 THE ELEMENTS.
Página 17
... opposite , shall be equal each to each , viz . the angle ABC to the B angle DEF , and the angle ACB to DFE . CE D Book 1 . - For , if the triangle ABC be applied to DEF , so that the poi A may be on D , and the straight line AB upon DE ...
... opposite , shall be equal each to each , viz . the angle ABC to the B angle DEF , and the angle ACB to DFE . CE D Book 1 . - For , if the triangle ABC be applied to DEF , so that the poi A may be on D , and the straight line AB upon DE ...
Página 18
... opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF ...
... opposite ; therefore the angle FBC is equal to the angle GCB , and the angle BCF to the angle CBG : and , since it has been demonstrated , that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF ...
Página 24
... opposite sides of it , make the adjacent angles together equal to two right angles , these two . straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD ...
... opposite sides of it , make the adjacent angles together equal to two right angles , these two . straight lines shall be in one and the same straight line . At the point B in the straight line AB , let the two straight lines BC , BD ...
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Términos y frases comunes
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