Elements of Geometry |
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Page 2
... sides is the most simple of these figures , and is called a triangle ; that of four sides is called a quadrilateral ; that of five sides , a pentagon ; that of six , a hexa- gon , & c . 15. A triangle is denominated equilateral ( fig ...
... sides is the most simple of these figures , and is called a triangle ; that of four sides is called a quadrilateral ; that of five sides , a pentagon ; that of six , a hexa- gon , & c . 15. A triangle is denominated equilateral ( fig ...
Page 3
... sides equal ; an equiangular polygon is one which has all its angles equal . 20. Two polygons are equilateral with respect to each other , when they have their sides equal , each to each , and placed in the same order , that is , when ...
... sides equal ; an equiangular polygon is one which has all its angles equal . 20. Two polygons are equilateral with respect to each other , when they have their sides equal , each to each , and placed in the same order , that is , when ...
Page 7
... sides and the included angle of the one are equal to two sides and the included angle of the other , each to each . Demonstration . In the two triangles ABC , DEF ( fig . 2. ) , let Fig . 23- the angle A be equal to the angle D , the side ...
... sides and the included angle of the one are equal to two sides and the included angle of the other , each to each . Demonstration . In the two triangles ABC , DEF ( fig . 2. ) , let Fig . 23- the angle A be equal to the angle D , the side ...
Page 8
... sides , the sum of these lines will be less than that of AB , AC , the two other sides . Demonstration . Let BO be produced till it meet the side AC in D ; the straight line OC is less than OD + DC ; to each of these add BO , and BO + ...
... sides , the sum of these lines will be less than that of AB , AC , the two other sides . Demonstration . Let BO be produced till it meet the side AC in D ; the straight line OC is less than OD + DC ; to each of these add BO , and BO + ...
Page 9
... sides AB , AC , are equal to the sides DE , DF , each to each , the side BC would be greater than EF ( 42 ) ; and if the angle A were less than the angle D , then the side BC would be less than EF ; but BC is equal to EF , therefore the ...
... sides AB , AC , are equal to the sides DE , DF , each to each , the side BC would be greater than EF ( 42 ) ; and if the angle A were less than the angle D , then the side BC would be less than EF ; but BC is equal to EF , therefore the ...
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Common terms and phrases
ABC fig adjacent angles altitude angle ACB angle BAD 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 and parallel equiangular equilateral equivalent faces figure four right angles frustum Geom gles greater hence homologous sides hypothenuse inclination inscribed circle isosceles join less let fall line AC manner mean proportional measure the half meet multiplied number of sides oblique lines opposite parallelogram parallelopiped perimeter perpendicular plane MN polyedron prism proposition pyramid S-ABC quadrilateral radii radius ratio rectangle regular polygon right angles right-angled triangle Scholium segment semicircumference side BC similar solid angle sphere spherical polygons spherical triangle square described straight line tangent THEOREM three plane angles triangle ABC triangular prism triangular pyramids vertex vertices whence