Elements of Geometry |
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Page 11
... whence the angle C can be neither less than B , nor equal to it ; it is therefore greater . THEOREM . 50. From a given point A ( fig . 31 ) , without a straight line Fig . 3k , DE , only one perpendicular can be drawn to that line ...
... whence the angle C can be neither less than B , nor equal to it ; it is therefore greater . THEOREM . 50. From a given point A ( fig . 31 ) , without a straight line Fig . 3k , DE , only one perpendicular can be drawn to that line ...
Page 12
... Whence each point in the perpendicular EF is equally distant from the extremities of the line AB . 2. Let I be a point out of the perpendicular ; join IA , IB , one of these lines must cut the perpendicular in D ; join DB , then ᎠᏴ ...
... Whence each point in the perpendicular EF is equally distant from the extremities of the line AB . 2. Let I be a point out of the perpendicular ; join IA , IB , one of these lines must cut the perpendicular in D ; join DB , then ᎠᏴ ...
Page 13
... whence AG AC . But AG cannot be equal to AC ( 52 ) ; therefore it is impossible that BC should be unequal to EF , that is , it is equal to it , and the triangle ABC is equal to the triangle DEF . : THEOREM . 57. In any triangle , the ...
... whence AG AC . But AG cannot be equal to AC ( 52 ) ; therefore it is impossible that BC should be unequal to EF , that is , it is equal to it , and the triangle ABC is equal to the triangle DEF . : THEOREM . 57. In any triangle , the ...
Page 23
... , each to each , and are consequently equal ; whence it follows , that the angle AOB BOC , and that thus the two diagonals of a rhom- bus cut each other mutually at right angles . Fig . 46 . Fig . 47 . SECTION SECOND Of Parallelograms . 23.
... , each to each , and are consequently equal ; whence it follows , that the angle AOB BOC , and that thus the two diagonals of a rhom- bus cut each other mutually at right angles . Fig . 46 . Fig . 47 . SECTION SECOND Of Parallelograms . 23.
Page 30
... whence the arc MH = HP , and the arc NH = HQ ; also MH - NH HP - HQ , that is , MN PQ . = = 2. If , of the two parallels AB , DE ( fig . 56 ) , one be a secant and the other a tangent , to the point of contact H draw the ra- dius CH ...
... whence the arc MH = HP , and the arc NH = HQ ; also MH - NH HP - HQ , that is , MN PQ . = = 2. If , of the two parallels AB , DE ( fig . 56 ) , one be a secant and the other a tangent , to the point of contact H draw the ra- dius CH ...
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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