 | Thomas Keith - 1839 - 498 pàgines
...when compared 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 - 1841 - 244 pàgines
...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 - 1845 - 894 pàgines
...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 - 1845 - 506 pàgines
...OBNDO, whose angle is BOD. PBOPOSITION 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 - 1845 - 542 pàgines
...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... | |
 | George Roberts Perkins - 1847 - 326 pàgines
...whose angle is BOD. Y PROPOSITION XXXV. THEOREM. The surface of any spherical triangle is measured by the excess of the sum of its three angles above two right angles. Let ABC be the proposed triangle : produce its sides till they meet the great circle DEFG, drawn anywhere... | |
 | James Hann - 1849 - 80 pàgines
...sides are very small with respect to the radius of the earth, if from each of its angles one-third of the excess of the sum of its three angles above...be taken for the angles of a rectilinear triangle, the sides of which are equal in length to those of the proposed spherical triangle, or in other terms... | |
 | James Hann - 1849 - 82 pàgines
...consequently, by addition, or г2 (а + b + c — 180°). Hence the area of a spherical triangle is equal to the excess of the sum of its three angles above two right angles, which is called the spherical excess. The late Professor Woodhouse, in his able work on Trigonometry,... | |
 | Charles Davies - 1849 - 372 pàgines
...whose angle is BOD. PROPOSITION XX. THEOREM. The surface of a spherical triangle is measured by tIte 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... | |
 | Adrien Marie Legendre - 1852 - 436 pàgines
...ungula whose angle is BOD. PROPOSITION XVIII. THEOEEM. The surface of a spherical triangle is equal to the excess of the sum of its' three angles above two right angles, multiplied by the tri-rectangular triangle. Let ABC be any spherical triangle : then will its surface... | |
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... third of the excess of the sum of its three angles above two right angles... 
