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" ... this 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 it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described... "
A Series on Elementary and Higher Geometry, Trigonometry, and Mensuration ... - Page 14
by Nathan Scholfield - 1845
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1828 - 346 pages
...in which case, the centres and the point of contact lie in the same straight line. THEOREM. i 471. The angle formed by two arcs of great circles, is equal to the angle formed by the tangents of these arcs at their point of intersection, and is measured by the arc described from this point of intersection,...
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Elements of Geometry and Trigonometry: With Notes

Adrien Marie Legendre - Geometry - 1830 - 344 pages
...the tangents of these arcs at their point of intersection, and is measured by the arc describedfrom this point of intersection, as a pole, and limited...by the sides, produced if necessary. Let the angle BAC be formed by the A.. two arcs AB, AC ; then will it be equal to the angle FAG formed by the tangents...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1836 - 359 pages
...pole with which a perpendicular to AM may be described passing through the point P. PROPOSITION VI. THEOREM. The angle formed by two arcs of great circles, is equal to the angle formed by the tangents nf these arcs at their point of intersection, and is measured by the arc described from this point...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1837 - 359 pages
...may be described passing through the point P. PROPOSITION VI. THEOREM. The angle formed by two area of great circles, is equal to the angle formed by the tangents oftliese arcs at their point of intersection, and is measured by the arc described from this point...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 384 pages
...pole with which a perpendicular to AM may be described passing through the point P. PROPOSITION VI. THEOREM. The angle formed by two arcs of great circles,...equal to the angle formed by the tangents of these arcs at their point of intersection, and is measured by the arc described from this point of intersection,...
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Elements of Geometry and Trigonometry

Adrien Marie Legendre - Geometry - 1838 - 386 pages
...perpendicular to AM may be described passing through the point P. PROPOSITION VI. THEOREM. The angle fanned by two arcs of great circles, is equal to the angle formed by trie tangents of these arcs at their point of intersection, and is measured by the arc described from...
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Elements of plane (solid) geometry (Higher geometry) and trigonometry (and ...

Nathan Scholfield - 1845 - 896 pages
...in which case, the centres and the point of contact lie in the same straight line. PROPOSITION VIII. THEOREM. The angle formed by two arcs of great circles,...the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described about A as a pole....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Geometry - 1845 - 506 pages
...in which case, the centres and the point of contact lie in the same straight line. PROPOSITION VIII. THEOREM. The angle formed by two arcs of great circles,...the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents AF, AG, and be measured by the arc DE, described about A as a pole....
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Higher Geometry and Trigonometry: Being the Third Part of a Series on ...

Nathan Scholfield - Conic sections - 1845 - 244 pages
...in which case, the centres and the point of contact lie in the same straight line. PROPOSITION VIII. THEOREM. The angle formed by two arcs of great circles,...by the sides, produced if necessary. Let the angle BAC be formed by the two arcs AB, AC ; then it will be equal to the angle FAG formed by the tangents...
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Elements of Geometry: With Practical Applications ...

George Roberts Perkins - Geometry - 1847 - 308 pages
...and the point of contact lie in the same straight line. • '•'.•',.' ' ii ** , PROPOSITION XXI. THEOREM. The angle formed by two arcs of great circles...equal to the angle formed by the tangents of these arcs at the point of intersection, and is therefore measured by the arc described from the point of...
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