...becomes very great for two places widely separated on the same parallel of latitude far from the equator. A great circle is the intersection of the surface of a sphere and a plane through the center of the sphere. It is the largest circle that can be drawn on the surface...

...lines of intersection ' or ' arrises ' at the common point, through which the three planes pass. It jis usual, and convenient, to assume that the three intersecting...radius is therefore, equal to that of the sphere, ride Part I.). A ' spherical triangle ' may, therefore, be represented in orthographic projection in...

...SPHER1CAL trigonometry ' might be called ' Solid trigonometry,' Ken1arks ° ^ >n contradistinction to ' Plane trigonometry,' which deals with the ratios...the intersection of the surface of a sphere with a [4ane passing through the centre. Its radius is, therefore, equal to that of the sphere, fide Part...

...interprets "point" to be a point on a sphere and "straight line" to be a great circle (ie, by definition, the intersection of the surface of a sphere with a plane passing through its center). In this model, any two "lines" intersect, so there are no parallels to a given "line"...