Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added, Elements of Plane and Spherical TrigonometryB. & S. Collins; W. E. Dean, printer, 1836 - 311 páginas |
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... fall to the share either of himself , or of any other of the moderns . But , after all this was accomplished , something still remained to be done , since , notwithstanding the acknowledged excellence of EUCLID'S Ele- ments , it could ...
... fall to the share either of himself , or of any other of the moderns . But , after all this was accomplished , something still remained to be done , since , notwithstanding the acknowledged excellence of EUCLID'S Ele- ments , it could ...
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... fall exactly on the equal side EF . Then , since the angle B is equal to the angle E ( by hyp . ) the side BA must fall on the side ED ; and , in like manner , because the angle C is equal to the angle F , the side AC must fall on the ...
... fall exactly on the equal side EF . Then , since the angle B is equal to the angle E ( by hyp . ) the side BA must fall on the side ED ; and , in like manner , because the angle C is equal to the angle F , the side AC must fall on the ...
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... fall on their intersection D ; consequently , the two triangles BAC , EDF , are identical , or mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles these three things are equal , namely , BC = EF , B = E , and C = F , it ...
... fall on their intersection D ; consequently , the two triangles BAC , EDF , are identical , or mutually equal ( Ax . 8. ) . COROLLARY . Whenever in two triangles these three things are equal , namely , BC = EF , B = E , and C = F , it ...
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... falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF ...
... falling upon two other straight lines makes the alternate angles equal to one another , these two straight lines are parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF ...
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... fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together ...
... fall upon two parallel straight lines , it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite upon the same side ; and likewise the two interior angles upon the same side together ...
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Términos y frases comunes
ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC angles equal base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated diameter divided equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROP proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR third touches the circle triangle ABC triangle DEF wherefore