 | Adrien Marie Legendre - Geometry - 1836 - 394 pages
...together equivalent to the spherical ungula whose angle is BOD. PROPOSITION XX. THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle. Let ABC be the proposed triangle : produce its sides till... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 92 pages
...2 A. Therefore the (890) sum of ABC and DEF is also measured by 2 A. 87. Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three (891) angles over two right angles or 180°. Demonstration. Let ABC (fig. 10.) be the given triangle.... | |
 | Benjamin Peirce - Spherical trigonometry - 1836 - 84 pages
...2 A. Therefore the(890) sum of AB С and DEF is also measured by 2 A. 87. Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three (891) angles over two right angles or 180°. Demonstration. Let ABC (fig. 10.) be the given triangle.... | |
 | Adrien Marie Legendre - Geometry - 1837 - 376 pages
...equivalent to the spherical ungula whose angle is BOD. PROPOSITION XX. THEOREM. The surface of a splierical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle. Let ABC be the proposed triangle : produce' its sides till... | |
 | Benjamin Peirce - Geometry - 1837 - 216 pages
...measured by 2 A. Therefore the sum of ABC and DEF is also measured by 2 A. 468. Theorem. The surface of a spherical triangle is measured by the excess of the sum of its three angles over two right angles, or 180°. Demonstration. Let ABC (fig. 190) be the given triangle. Produce AC... | |
 | Adrien Marie Legendre - Geometry - 1838 - 372 pages
...whose angle is BOD. PROPOSITION XX. THEOREM. The surface of a spherical triangle is measured by tlte excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle. Let ABC be the proposed triangle : produce its sides till... | |
 | Thomas Keith - 1839 - 498 pages
...with the radius of the sphere, being proposed ; if from each of its angles you subtract one third of the excess of the sum of its three angles above two right angles, the angles thus diminished may be taken for the angles of a rectilineal triangle, whose sides are equal... | |
 | John Hymers - Logarithms - 1841 - 244 pages
...sphere. 14. The area of a spherical triangle is the same fraction of the area of a hemisphere, that the excess of the sum of its three angles above two right angles is of ЗбО°. Let ABC (fig. 5.) be a spherical triangle; produce the arcs which contain its angles... | |
 | Nathan Scholfield - Conic sections - 1845 - 244 pages
...BOD is equivalent to the lune OBNDO, whose angle is BOD. PROPOSITION XXII. THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle. Let ABC be the proposed triangle : produce its sides till... | |
 | Nathan Scholfield - Conic sections - 1845 - 542 pages
...together equivalent to the spherical ungula whose angle is BOD. PROPOSITION XXH. THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle. Let ABC be the proposed triangle : produce its sides till... | |
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THEOREM. The surface of a spherical triangle is measured by the excess of the sum of its three angles above two right angles, multiplied by the tri-rectangular triangle. 
