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" The angle of two arcs of great circles is equal to the angle of their planes, and is measured by the arc of a great circle described from its vertex as a pole and included between its sides (produced if necessary). Let AB and AB... "
A Treatise on Elementary Geometry: With Appendices Containing a Collection ... - Σελίδα 244
των William Chauvenet - 1884 - 368 σελίδες
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An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1837 - 159 σελίδες
...-j- b -fc < 360ri. 441. Theorem. The angle formed by two arcs of great circles is measured by the arc described from its vertex as a pole, and included between its sides. Demonstration. The arc AM (fig. 177) measures the angle ACM, which, by art. 314, measures the angle...

An Elementary Treatise on Plane and Solid Geometry

Benjamin Peirce - 1847 - 150 σελίδες
...+ b -fc < 360°. 441. Theorem. The angle formed by two arcs of great circles is measured by the arc described from its vertex as a pole, and included between its sides. Proof. The arc AM (fig. 177) measures the angle •ACM, which, by 5) 315, measures the angle of the...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...Let the curves, AB and AB', on the surface of a sphere whose centre is O, intersect at A, and let AT and AT' be the tangents to the two curves, respectively....curves AB, AB', themselves; consequently the angle BAB', or TA T', is equal to the angle of these planes (56), the edge of this angle being the common...

A Treatise on Elementary Geometry: With Appendices Containing a Collection ...

William Chauvenet - 1871 - 368 σελίδες
...angle of two arcs of great circles is equal to the angle of their planes, and is measured by the are of a great circle described from its vertex as a pole...necessary). Let AB and AB' be two arcs of great circles, A Tand AT' the tangents to these arcs at A, O the centre of the sphere. The planes passing through...

Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1871 - 58 σελίδες
...tangents of those arcs at the point of their intersection; and is measured by the arc of a great cir cle described from its vertex as a pole, and included between its sides. HOOK IX. gents of these arcs at the point A and it is measured by the arc DB described from the vertex...

The Register, Cornell University

Cornell University - 1875
...equal to the angle of their planes, and is measured by the arc of a great circle described from the vertex as a pole and included between its sides (produced if necessary). 4. The diameter of a sphere is 20 inches. Find its convex surface, its volume, and the area of a zone...

Catalogue - Harvard University

Harvard University - 1876
...a circle, every section made by a plane parallel to the base is a circle. 6. The angle of two ores of great circles is equal to the angle of their planes,...included between its sides (produced if necessary). 7. In two polar triangles, each angle of one is measured by the supplement of the side lying opposite...

Elements of Geometry and the First Principles of Modern Geometry

Wm. H. H. Phillips - 1878 - 209 σελίδες
...the angle of two arcs of great circles has the same measure as the dihedral of their planes, or as the arc of a great circle described from its vertex...included between its sides (produced, if necessary). COR. 2. If two arcs of great circles cut each other, their vertical angles arc equal. COR. 3. If A...

Chauvenet's Treatise on Elementary Geometry

William Chauvenet - 1887 - 322 σελίδες
...space, whether drawn in the same plane or upon a surface of any kind. PROPOSITION IX.—THEOREM. 41. The angle of two arcs of great circles is equal to...circles, AT and AT' the tangents to these arcs at A, and O the centre of the sphere. TA and T'A lie in the planes of their arcs, and are perpendicular to...

Chauvenet's Treatise on Elementary Geometry

William Chauvenet - 1887 - 322 σελίδες
...space, whether drawn in the same plane or upon a surface of any kind. PROPOSITION IX.— THEOREM. 41. The angle of two arcs of great circles is equal to...Let AB and AB' be two arcs of great circles, AT and A I" the tangents to these arcs at A, and O the centre of the sphere. TA and T'A lie in the planes...




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