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 sider |
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Side 19
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . A E B G D C F For , if it be not parallel , AB and CD being produced ...
... parallel . Let the straight line EF , which falls upon the two straight lines AB , CD make the alternate angles AEF , EFD equal to one another ; AB is parallel to CD . A E B G D C F For , if it be not parallel , AB and CD being produced ...
Side 20
... parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXI . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
... parallel to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be parallel to each other . PROP . XXI . THEOR . If a straight line fall upon two parallel straight lines , it makes the alternate ...
Side 21
... parallel ; for the angles KGH , GHC would then be equal to two right angles . Neither do they meet on the other side ... parallel , and since they do not meet towards L and D , they must meet if produced towards K and C. COR . Through a ...
... parallel ; for the angles KGH , GHC would then be equal to two right angles . Neither do they meet on the other side ... parallel , and since they do not meet towards L and D , they must meet if produced towards K and C. COR . Through a ...
Side 22
... parallel , each to each , and lying in the same direction . If the straight lines AB , AC be parallel to DF , DE ; the angle BAC is equal to EDF . For , draw GAD through the vertices . And since AB is parallel to DF , the ex- terior ...
... parallel , each to each , and lying in the same direction . If the straight lines AB , AC be parallel to DF , DE ; the angle BAC is equal to EDF . For , draw GAD through the vertices . And since AB is parallel to DF , the ex- terior ...
Side 23
... parallel to the straight line AB ; and because AB is parallel to CE , and AC meets them , the al- ternate angles BAC , ACE are equal ( 21. 1. ) Again , because AB is parallel to CE , and BD falls upon them , the exterior an- gle ECD is ...
... parallel to the straight line AB ; and because AB is parallel to CE , and AC meets them , the al- ternate angles BAC , ACE are equal ( 21. 1. ) Again , because AB is parallel to CE , and BD falls upon them , the exterior an- gle ECD is ...
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Vanlige uttrykk og setninger
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