Elements of Geometry |
From inside the book
Results 6-10 of 47
Page 17
... proposition to poly- gons , which have any re - entering * angles , each of these angles is to be considered as greater than two right angles . But , in order to avoid confusion , we shall confine ourselves in future to those polygons ...
... proposition to poly- gons , which have any re - entering * angles , each of these angles is to be considered as greater than two right angles . But , in order to avoid confusion , we shall confine ourselves in future to those polygons ...
Page 20
... propositions as already demonstrated . 1. The two interior angles upon the same side , taken togeth- er , are equal to two right angles . 2. The alternate - internal angles are equal , as also the internal- external , and the alternate ...
... propositions as already demonstrated . 1. The two interior angles upon the same side , taken togeth- er , are equal to two right angles . 2. The alternate - internal angles are equal , as also the internal- external , and the alternate ...
Page 21
... proposition , name- ly , that the side EF be directed the same way as AC , and ED the same way as AB : the reason is this ; if we produce FE toward H , the angle DEH would have its sides parallel to those of the angle BAC , but the two ...
... proposition , name- ly , that the side EF be directed the same way as AC , and ED the same way as AB : the reason is this ; if we produce FE toward H , the angle DEH would have its sides parallel to those of the angle BAC , but the two ...
Page 30
... proposition admits of three cases . per- 1. If the two parallels are secants , draw the radius CH pendicular to the chord MP , it will also be perpendicular to its parallel NQ ( 74 ) , and the point I will be at the same time the middle ...
... proposition admits of three cases . per- 1. If the two parallels are secants , draw the radius CH pendicular to the chord MP , it will also be perpendicular to its parallel NQ ( 74 ) , and the point I will be at the same time the middle ...
Page 33
... proposition enunciated be not true , the angle ACB will be to the angle ACD as the arc AB is to an arc greater or less than AD . Let this arc be supposed to be greater , and let it be represented by AO ; we shall have , angle ACB ...
... proposition enunciated be not true , the angle ACB will be to the angle ACD as the arc AB is to an arc greater or less than AD . Let this arc be supposed to be greater , and let it be represented by AO ; we shall have , angle ACB ...
Other editions - View all
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