Elements of Geometry |
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Page 107
... inclination of two planes , is the quantity , whether greater or less , by which they depart from each other ; this quantity is measured by the angle contained by two straight lines drawn from the same point per- pendicularly to the ...
... inclination of two planes , is the quantity , whether greater or less , by which they depart from each other ; this quantity is measured by the angle contained by two straight lines drawn from the same point per- pendicularly to the ...
Page 110
... inclination of the oblique line AB to the plane MN . It is manifest that this in- clination is the same for all the oblique lines AB , AC , AD , & c . , which depart equally from the perpendicular ; for all the trian- gles ABP , ACP ...
... inclination of the oblique line AB to the plane MN . It is manifest that this in- clination is the same for all the oblique lines AB , AC , AD , & c . , which depart equally from the perpendicular ; for all the trian- gles ABP , ACP ...
Page 119
... inclination to each other as the planes of the homologous angles in the other . Demonstration . Let the angle ASC = DTF ( fig . 197 ) , the Fig . 97 . angle ASB = DTE , and the angle BSC = ETF ; we say that the two planes ASC , ASB ...
... inclination to each other as the planes of the homologous angles in the other . Demonstration . Let the angle ASC = DTF ( fig . 197 ) , the Fig . 97 . angle ASB = DTE , and the angle BSC = ETF ; we say that the two planes ASC , ASB ...
Page 120
... inclination of the two planes DTE , DTF ; therefore these two inclinations are equal to each other . It should be observed , however , that the angle A of the right- angled triangle OAB is not properly the inclination of the two planes ...
... inclination of the two planes DTE , DTF ; therefore these two inclinations are equal to each other . It should be observed , however , that the angle A of the right- angled triangle OAB is not properly the inclination of the two planes ...
Page 122
... inclination of the planes SAB , SAC , in the solid angle . When the point O falls between A and B ' in the plane figure , the angle EA b becomes obtuse , and always measures the true inclination of the planes . It is on this account ...
... inclination of the planes SAB , SAC , in the solid angle . When the point O falls between A and B ' in the plane figure , the angle EA b becomes obtuse , and always measures the true inclination of the planes . It is on this account ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAC base ABCD bisect centre chord circ circular sector circumference circumscribed common cone consequently construction convex surface Corollary cube cylinder Demonstration diagonals diameter draw drawn equal angles equiangular equilateral equivalent faces figure formed four right angles frustum GEOM given point gles greater hence homologous sides hypothenuse inclination intersection isosceles triangle JOHN CRERAR LIBRARY join less Let ABC let fall line AC mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism produced proposition radii radius ratio rectangle regular polygon right angles Scholium sector segment semicircle semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three angles triangle ABC triangular prism triangular pyramids vertex vertices whence