The Elements of EuclidJohnson and Warner, 1811 - 518 páginas |
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Página 196
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles to a plane , when it makes right angles with every straight line ...
... SOLID is that which hath length , breadth , and thickness . II . That which bounds a solid is a superficies . III . A straight line is perpendicular , or at right angles to a plane , when it makes right angles with every straight line ...
Página 197
... angles of inclination are equal to one another . VIII Parallel planes are such which do not meet one another though produced . IX . A solid angle is that which is made by the meeting of more See Note than two plane angles , which are ...
... angles of inclination are equal to one another . VIII Parallel planes are such which do not meet one another though produced . IX . A solid angle is that which is made by the meeting of more See Note than two plane angles , which are ...
Página 198
... angle , which revolves . XXI . A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides , which re- mains fixed . XXII . The axis of a cylinder is the fixed straight line about ...
... angle , which revolves . XXI . A cylinder is a solid figure described by the revolution of a right angled parallelogram about one of its sides , which re- mains fixed . XXII . The axis of a cylinder is the fixed straight line about ...
Página 213
Euclid Robert Simson. Book XI . PROP . XX . THEOR . IF a solid angle be contained by three plane angles , See Note , any two of them are greater than the third . Let the solid angle at A be contained by the three plane angles BAC , CAD ...
Euclid Robert Simson. Book XI . PROP . XX . THEOR . IF a solid angle be contained by three plane angles , See Note , any two of them are greater than the third . Let the solid angle at A be contained by the three plane angles BAC , CAD ...
Página 214
... solid angle at B is contained by the three plane angles CBA , ABD , DBC , any two of them are greater than the third ; therefore the angles CBA , ABD are greater than the angle DBC : for the same reason , the angles BCA , ACD are ...
... solid angle at B is contained by the three plane angles CBA , ABD , DBC , any two of them are greater than the third ; therefore the angles CBA , ABD are greater than the angle DBC : for the same reason , the angles BCA , ACD are ...
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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