...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 ayjgles thus diminished may be taken for the angles of a rectilinear triangle, whose sides are...

...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 two right angles be subtracted, tlie angles so diminished may be taken for the angles of a rectilinear triangle, •wJwse...

...sides are very tmall, compared with the radius of the sfihere ; if from each of its angles tne third of the excess of the sum of its three angles above two right angles be subtracted^ the angles so diminished may be taken for the angles of a rectilinear triangle^ whose...

...sides are very small, compared with the radius of the sphere; if from, each of it's angles one third of the excess of the sum of its three angles above two right angles be subtracted, the angles so diminished may be taken for the angles of a rectilinear triangle, whose...

...sides are very small relatively to the radius of the sphere, if from each of its angles one-third of the excess of the sum of its three angles above two right angles be subtracted, the angles so diminished may be taken for the angles of a rectilinear triangle, the...

...whose angle is BOD. PROPOSITION XXIII. 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...

...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...

...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...

...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 two right angles be subtracted, the angles so diminished may be taken for the angles of a rectilineal triangle, whose...

...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...