 | Thomas Keith - 1826 - 504 pages
...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 rectilinear triangle, whose sides are equal... | |
 | Thomas Leybourn - 1830 - 630 pages
...given in terms of а, Ъ, с, and d. Again, since the area of a spherical triangle is proportional to the excess of the sum of its three angles above two right angles, technically termed the spherical excess, which (spherical excess) by Simon Lhuillier's Theorem, may... | |
 | John Farrar - 1833 - 274 pages
...its angles we subtract a third of the excess of the sum of the three angles over two right angles, the angles so diminished may be taken for the angles of a plane triangle, the sides of which are equal in length to those of the spherical triangle. In other... | |
 | John Farrar - 1833 - 276 pages
...its angles we subtract a third of the excess of the sum of the three angles over two right angles, the angles so diminished may be taken for the angles of a plane triangle, the sides of which are equal in length to those of the spherical triangle. In other... | |
 | William Galbraith - 1834 - 454 pages
...sides are very small compared with the radius of the sphere ; if from each of its angles, one-third of the excess of the sum of its three angles, above...angles so diminished may be taken for the angles of a rectilineal triangle, whose sides are equal in length to those of the proposed triangle. To find the... | |
 | Adrien Marie Legendre - 1836 - 394 pages
...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... | |
 | Adrien Marie Legendre - 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
...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 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... | |
 | John Gregory - 1842 - 328 pages
...angles you subtract one third of the excess of the sum of its three angles above 180°, the angles thus diminished may be taken for the angles of a rectilinear triangle, whose sides are equal in length to those of the proposed spherical triangle. The preceding proposition is illustrated by the following... | |
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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. 
