Elements of Geometry |
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Page 6
... taken together , are equal to two right angles ; also the other angles ACD , BCD , are together equal to two right angles . In general , if any number of straight lines , as CA , CB ( fig . 22 ) , & c . , meet in the same point C , the ...
... taken together , are equal to two right angles ; also the other angles ACD , BCD , are together equal to two right angles . In general , if any number of straight lines , as CA , CB ( fig . 22 ) , & c . , meet in the same point C , the ...
Page 10
... taken indifferently for a base ; and then its vertex is that of the opposite angle . In an isosceles triangle , the base is that side which is not equal to one of the others . THEOREM . 48. Reciprocally , if two angles of a triangle are ...
... taken indifferently for a base ; and then its vertex is that of the opposite angle . In an isosceles triangle , the base is that side which is not equal to one of the others . THEOREM . 48. Reciprocally , if two angles of a triangle are ...
Page 20
... taken togeth- er , are equal to two right angles . 2. The alternate - internal angles are equal , as also the internal- external , and the alternate - external . . Reciprocally , if , in this second case , two angles of the same name ...
... taken togeth- er , are equal to two right angles . 2. The alternate - internal angles are equal , as also the internal- external , and the alternate - external . . Reciprocally , if , in this second case , two angles of the same name ...
Page 32
... taken equal to DCE ; and we have , according to what has just been demonstrated , AIDE . But , by hy- pothesis , the arc AB DE ; we should consequently have AI = AB , or the part equal to the whole , which is impossible ; therefore the ...
... taken equal to DCE ; and we have , according to what has just been demonstrated , AIDE . But , by hy- pothesis , the arc AB DE ; we should consequently have AI = AB , or the part equal to the whole , which is impossible ; therefore the ...
Page 34
... taken in the same circle , or in equal circles , ≈re to each other as the arcs AB , AD , the bases of these sectors . It will be perceived , therefore , that the arcs of a circle , which are used as a measure of angles , will also ...
... taken in the same circle , or in equal circles , ≈re to each other as the arcs AB , AD , the bases of these sectors . It will be perceived , therefore , that the arcs of a circle , which are used as a measure of angles , will also ...
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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