Elements of Geometry |
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Page 7
... THEOREM . 38. Two triangles are equal , when a side and the two adjacent angles of the one are equal to a side and the two adjacent angles of the other , each to each . Demonstration . Let the side BC ( fig . 23 ) be equal to the side ...
... THEOREM . 38. Two triangles are equal , when a side and the two adjacent angles of the one are equal to a side and the two adjacent angles of the other , each to each . Demonstration . Let the side BC ( fig . 23 ) be equal to the side ...
Page 8
... THEOREM . 40. One side of a triangle is less than the sum of the other two . Demonstration . The straight line BC ( fig . 23 ) , for example , is the shortest way from B to C ( 3 ) ; BC therefore is less than BA + AC . THEOREM . 41. If ...
... THEOREM . 40. One side of a triangle is less than the sum of the other two . Demonstration . The straight line BC ( fig . 23 ) , for example , is the shortest way from B to C ( 3 ) ; BC therefore is less than BA + AC . THEOREM . 41. If ...
Page 9
... THEOREM . 43. Two triangles are equal , when the three sides of the one are equal to the three sides of the other , each to each . Demonstration . Let the side AB = DE ( fig . 23 ) , AC = DF , Fig . 23 . BC = EF ; then the angles will ...
... THEOREM . 43. Two triangles are equal , when the three sides of the one are equal to the three sides of the other , each to each . Demonstration . Let the side AB = DE ( fig . 23 ) , AC = DF , Fig . 23 . BC = EF ; then the angles will ...
Page 10
... THEOREM . 48. Reciprocally , if two angles of a triangle are equal , the op- posite sides are equal , and the triangle is isosceles . Demonstration . Let the angle ABC ACB ( fig . 29 ) , the side AC will be equal to the side AB . For ...
... THEOREM . 48. Reciprocally , if two angles of a triangle are equal , the op- posite sides are equal , and the triangle is isosceles . Demonstration . Let the angle ABC ACB ( fig . 29 ) , the side AC will be equal to the side AB . For ...
Page 11
... 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 Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that ...
... 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 Demonstration . If it be possible , let there be two AB and AC ; produce one of them AB , so that ...
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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