...therefore its Diameter is equal, &c. Q;E. D, PROP. PROP. VII. . In the Stereographick ProjettionjheAngles made by the Circles on the Surface of the Sphere, are equal to the Angles made by their RefrefentAtivej in the of the Projection. Suppofe the Eye at A projecting the Angle RBS upon the Primitive...

...common to both, there will remain CBA=DBE*e = FBI. ?. e. d, PROP. V. i Tn Stenographic Projeftiott the Angles made by the Circles on the Surface of the Sphere are equal to the Angles made by their Reprefentatiyes on the plane of the Projection. DEMONSTRATION. Suppofe the Eye at A, projsfting the...

...primitive Circle, as well as within it •-, and alfo the Angles made by the Interfeclion of two great Circles on the Surface of the Sphere, are equal to the Angles made by their Reprefentatives on the Plain of the Projection. In any projection, that Circle upon whofe Plain the...

...Point, deduc'd in the Fir ft Scholium to the Fourth Proportion. For as in Stenographic Projections, the Angles made by the Circles on the Surface of the Sphere, are equal to thofe made by their Reprefentatives upon the Plane of the Projection ; 'tis plain, that if we project...

...thofe Half-Tangents is Qa Therefore its Diameter is equal, ED THEOTHEOREM XI. In the Stereographic Projection, the Angles made by the Circles on the Surface of the Globe or Sphere, are equal to the Angles made by their Repreientations in the Plane of the Projection....

...7th. The angles made by circles intersecting each other on the plane of projection are always equal to the angles made by the circles on the surface of the sphere which they respectively represent. (73) From the foregoing properties, it results that, although the...