Elements of Geometry |
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Page 17
... polygons , which have only saliant angles , and which may be called convex polygons . Every convex polygon is such , that a straight line , however drawn , cannot meet the perimeter in more than two points . THEOREM . 69. If two ...
... polygons , which have only saliant angles , and which may be called convex polygons . Every convex polygon is such , that a straight line , however drawn , cannot meet the perimeter in more than two points . THEOREM . 69. If two ...
Page 25
... polygon is said to be circumscribed about a circle , when all its sides are tangents to the circumference ; and in this case the circle is said to be inscribed in the polygon . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects the ...
... polygon is said to be circumscribed about a circle , when all its sides are tangents to the circumference ; and in this case the circle is said to be inscribed in the polygon . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects the ...
Page 65
... polygons are composed of the same number of triangles , which are similar to each other , and similarly dis- posed ... polygon FGHIK draw , in like manner , from the angle F , homologous to A , the diagonals FH , FI , to the other ...
... polygons are composed of the same number of triangles , which are similar to each other , and similarly dis- posed ... polygon FGHIK draw , in like manner , from the angle F , homologous to A , the diagonals FH , FI , to the other ...
Page 66
... polygons ; therefore two similar polygons are composed of the same number of triangles , which are similar to each other , and similarly disposed . 220. Scholium . The converse of this proposition is equally true ; if two polygons are ...
... polygons ; therefore two similar polygons are composed of the same number of triangles , which are similar to each other , and similarly disposed . 220. Scholium . The converse of this proposition is equally true ; if two polygons are ...
Page 67
... polygon ABCDE , is to the sum of consequents FGH + FHI + FIK , or the polygon FGHIK , as one antecedent ABC is to its consequent FGH , or as AB is to FG ( 219 ) . Therefore the surfaces of similar polygons are to each other as the ...
... polygon ABCDE , is to the sum of consequents FGH + FHI + FIK , or the polygon FGHIK , as one antecedent ABC is to its consequent FGH , or as AB is to FG ( 219 ) . Therefore the surfaces of similar polygons are to each other as the ...
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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