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 TrigonometryW. E. Dean, 1840 - 317 sider |
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Side 16
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle . FDC is likewise greater than BCD ...
... equal to AD in the triangle ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one another , but the angle ECD is greater than the angle BCD ; wherefore the angle . FDC is likewise greater than BCD ...
Side 17
... equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from ...
... equal ( 8. Ax . ) to it . PROP . IX . PROB . To bisect a given rectilineal angle , that is , to divide it into two equal angles . A Let BAC be the given rectilineal angle , it is required to bisect it . Take any point D in AB , and from ...
Side 18
... equal to the two EC , CF , each to each ; but the base DF is also equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) to the angle ECF ; and they are adjacent an- gles . But , when the adjacent angles which one straight ...
... equal to the two EC , CF , each to each ; but the base DF is also equal to the base EF ; therefore the angle DCF is equal ( 8. 1. ) to the angle ECF ; and they are adjacent an- gles . But , when the adjacent angles which one straight ...
Side 19
... equal to the two angles CBA , ABE together ; add the an- gle EBD to each of these equals , and the two angles CBE , EBD will be equal ( 2. Ax . ) to the three CBA , ABE , EBD . Again , the angle DBA is equal to the two angles DBE , EBA ...
... equal to the two angles CBA , ABE together ; add the an- gle EBD to each of these equals , and the two angles CBE , EBD will be equal ( 2. Ax . ) to the three CBA , ABE , EBD . Again , the angle DBA is equal to the two angles DBE , EBA ...
Side 20
... equal ( 13. 1. ) to two right angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining ...
... equal ( 13. 1. ) to two right angles ; but the angles ABC , ABD are likewise together equal to two right angles : therefore the angles CBA , ABE are equal to the angles CBA , ABD : Take away the common angle ABC , and the remaining ...
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ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional 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 touches the circle triangle ABC triangle DEF wherefore