Elements of Geometry |
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Page 4
... Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and ... fall upon A , and the point F upon B. These two lines , thus placed , will ... fall upon the point C , the middle of AB . The side GE being thus applied to ...
... Let the straight line CD be perpendicular to Fig . 16. AB ( fig . 16 ) , and ... fall upon A , and the point F upon B. These two lines , thus placed , will ... fall upon the point C , the middle of AB . The side GE being thus applied to ...
Page 7
... fall upon A , and the point E upon B. But , since the angle D is equal to ... Let the side BC ( fig . 23 ) be equal to the side Fig . 23 . EF , the angle ... let EF be placed upon its equal BC , the point E will fall upon B and the point ...
... fall upon A , and the point E upon B. But , since the angle D is equal to ... Let the side BC ( fig . 23 ) be equal to the side Fig . 23 . EF , the angle ... let EF be placed upon its equal BC , the point E will fall upon B and the point ...
Page 9
... fall upon the side BC , then Fig . 26 it is evident that GC , or its equal ... Let the side AB = DE ( fig . 23 ) , AC = DF , Fig . 23 . BC = EF ; then the ... Let the side AB = AC ( fig . 28 ) , then will Fig . 28 . the angle C be equal ...
... fall upon the side BC , then Fig . 26 it is evident that GC , or its equal ... Let the side AB = DE ( fig . 23 ) , AC = DF , Fig . 23 . BC = EF ; then the ... Let the side AB = AC ( fig . 28 ) , then will Fig . 28 . the angle C be equal ...
Page 17
... fall upon the case of the pre- ceding proposition . Let us suppose , then , that they are unequal ; and that , through the point F , the vertex of the greater , we let fall upon AB a perpendicular FG . In the triangle EFG , the sum of ...
... fall upon the case of the pre- ceding proposition . Let us suppose , then , that they are unequal ; and that , through the point F , the vertex of the greater , we let fall upon AB a perpendicular FG . In the triangle EFG , the sum of ...
Page 26
... fall upon G ; therefore the chord AD is equal to the chord EG . Conversely , AC being supposed equal to EO , if the ... Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and AH , and the radii CD , CH , be drawn ...
... fall upon G ; therefore the chord AD is equal to the chord EG . Conversely , AC being supposed equal to EO , if the ... Let the arc AH ( fig . 50 ) be greater than AD , and let the chords AD and AH , and the radii CD , CH , be drawn ...
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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