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" ... point of intersection, as a pole, and limited by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then... "
Higher Geometry and Trigonometry: Being the Third Part of a Series on ... - Page 14
by Nathan Scholfield - 1845 - 232 pages
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1863 - 464 pages
...quadjant DFA round the point D, its extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal tŪ that formed by the tangents to these arcs at their point of intersection, and is measured by the...
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Elements of Plane and Solid Geometry: And of Plane and Spherical ...

Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...without the sphere. Therefore the plane XYZ is a tangent to the sphere. PROPOSITION IV. The angles formed by two arcs of great circles is equal to the angle contained by the tangents drawn to these arcs at their point of intersection, and is measured by the...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies, Adrien Marie Legendre - Geometry - 1869 - 470 pages
...quadrant DFA round the point D, its extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal to that formed by the tangents to these arcs at their point of intersection, and is measured by the arc...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1871 - 302 pages
...radii ; in which case, the centers and the point of contact lie in on* straight line. PROPOSITION VII. THEOREM. The angle formed by two arcs of great circles, is equal to the angle formed by the tangents of those arcs at the point of their intersection; and is measured by the arc of a great cir cle described...
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Elements of Geometry and Trigonometry from the Works of A.M. Legendre ...

Charles Davies - Geometry - 1872 - 464 pages
...quadrant DFA round the point D, its extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal to that formed by the tangents to these arcs at their point of intersection, and is measured by the arc...
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Elements of Geometry and Trigonometry: From the Works of A.M. Legendre

Adrien Marie Legendre - Geometry - 1874 - 500 pages
...quadrant DFA round the point D, its 'extremity A will describe an arc of a great circle. PROPOSITION IV. THEOREM. The angle formed by two arcs of great circles, is equal to that formed by the tangents to these arcs at their point of intersection, and is measured by the arc...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Conic sections - 1877 - 458 pages
...be out of the arc of a great circle ADB. Therefore the shortest path, etc. • ... PROPOSITION VII. THEOREM. The angle formed by two arcs of great circles is equal to the an~ gle formed by the tangents of those arcs at the point of their intersection, and is measured by...
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Syllabus of Propositions in Geometry: Intended for Use in Preparing Students ...

Harvard University - Geometry - 1899 - 39 pages
...straight line joining the centres of the spheres, and the centre of which is in that line. THEOREM VII. The angle formed by two arcs of great circles is equal to the angle between the planes of the circles, and is measured by the arc of a great circle described from its...
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Solid Geometry

Fletcher Durell, Elmer Ellsworth Arnold - Geometry, Solid - 1917 - 220 pages
...sky as covered by a similar network of lines ? SOLID GEOMETRY. BOOK IX PROPOSITION VII. THEOREM 672. The angle formed by two arcs of great circles is equal to the angle between the planes of the circles, and is measured by the arc of a great circle described from its...
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Mathematics: Course of Study for Senior and Junior High Schools

Baltimore (Md.). Department of Education - Mathematics - 1924 - 182 pages
...perpendicular to the line which joins the centers of the spheres, and whose center is in that line. 10. The angle formed by two arcs of great circles is equal to the angle between the planes of the circles, and is measured by the arc of a great circle described from its...
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