Elements of Geometry |
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Page vi
... circle , treats of the most sim- ple properties of the circle , and those of chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are followed by the resolution of certain problems relating to ...
... circle , treats of the most sim- ple properties of the circle , and those of chords , of tangents , and of the measure of angles by the arcs of a circle . These two sections are followed by the resolution of certain problems relating to ...
Page vii
... circle . Two lemmas are employed as the basis of this measure , which is otherwise demonstrated after the manner of Archimedes . We have then given two methods of approximation for squaring the circle , one of which is that of James ...
... circle . Two lemmas are employed as the basis of this measure , which is otherwise demonstrated after the manner of Archimedes . We have then given two methods of approximation for squaring the circle , one of which is that of James ...
Page 21
... each , and are consequently equal ; whence it follows , that the angle AOB = BOC , and that thus the two diagonals of a rhombus cut each other mutually at right angles . Fig . 46 . SECTION SECOND . Of the Circle Of Parallelograms . 21.
... each , and are consequently equal ; whence it follows , that the angle AOB = BOC , and that thus the two diagonals of a rhombus cut each other mutually at right angles . Fig . 46 . SECTION SECOND . Of the Circle Of Parallelograms . 21.
Page 22
... circle is a curved line all the points of which are equally distant from a point within called the centre . The circle is the space terminated by this curved line * . 91. Every straight line CA , CE , CD ( fig . 46 ) , & c . drawn from ...
... circle is a curved line all the points of which are equally distant from a point within called the centre . The circle is the space terminated by this curved line * . 91. Every straight line CA , CE , CD ( fig . 46 ) , & c . drawn from ...
Page 23
... 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 the circle and its cir- Fig . 49 ...
... 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 the circle and its cir- Fig . 49 ...
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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