Elements of Geometry |
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Page 20
... 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 . 84. The opposite ...
... 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 . 84. The opposite ...
Page 23
... 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 . 60 . . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects ...
... 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 . 60 . . THEOREM . 98. Every diameter AB ( fig . 49 ) bisects ...
Page 63
... polygons are composed of the same number of triangles , which are similar to each other and similarly disposed ... 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 disposed ... polygon FGHIK draw , in like manner , from the angle F , homologous to A , the diagonals FH , FI , to the other ...
Page 64
... 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 65
... polygon ABCDE , is to the sum of consequents FGH + FHI + FIK , or the polygon FGHIK , -2 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 , -2 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 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