Elements of Geometry |
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Page 16
... four right angles ; therefore , if all the angles of a quadrilateral are equal , each of them will be a right angle , which justifies the definition of a square and rectangle ( 17 ) . 66. Corollary II . The sum of the angles of a ...
... four right angles ; therefore , if all the angles of a quadrilateral are equal , each of them will be a right angle , which justifies the definition of a square and rectangle ( 17 ) . 66. Corollary II . The sum of the angles of a ...
Page 19
... four angles AEF , BEF , CFE , EFD , will be equal to four right angles ; accord- ingly , if from this sum we subtract AEF + CFE , which is greater than two right angles , there will remain the sum BEF + EFD , less than two right angles ...
... four angles AEF , BEF , CFE , EFD , will be equal to four right angles ; accord- ingly , if from this sum we subtract AEF + CFE , which is greater than two right angles , there will remain the sum BEF + EFD , less than two right angles ...
Page 20
Adrien Marie Legendre. Fig . 39 . Fig . 40 . the four acute angles to one of the four obtuse angles , the sum will always be equal to two right angles . 76. Scholium . The angles of which we have been speaking , compared , two and two ...
Adrien Marie Legendre. Fig . 39 . Fig . 40 . the four acute angles to one of the four obtuse angles , the sum will always be equal to two right angles . 76. Scholium . The angles of which we have been speaking , compared , two and two ...
Page 32
... four times in the angle DCE . The partial angles ACm , m Cn , n Cp , & c . , DC x , x Cy , & c . , being equal to each other , the partial arcs A m , m n , np , & c . , D x , x y , & c . , will also be equal to each other ( 119 ) , and ...
... four times in the angle DCE . The partial angles ACm , m Cn , n Cp , & c . , DC x , x Cy , & c . , being equal to each other , the partial arcs A m , m n , np , & c . , D x , x y , & c . , will also be equal to each other ( 119 ) , and ...
Page 38
... four , eight , sixteen , & c . , equal parts . PROBLEM . 139. Through a given point A ( fig . 75 ) , to draw a straight line parallel to a given straight line BC . Solution . From the point A , as a centre , with a radius suffi- ciently ...
... four , eight , sixteen , & c . , equal parts . PROBLEM . 139. Through a given point A ( fig . 75 ) , to draw a straight line parallel to a given straight line BC . Solution . From the point A , as a centre , with a radius suffi- ciently ...
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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