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

...propned, of which the 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...

...compared with the radius of the sphere; iff rant each of zts angles one third of the excess of the sum oj its three angles above two right angles be subtracted, the angles so diminished may be taken J'or the angles of a rectilinear triangle, qiAose sides are equal in length to those of the proposed...

...the 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...rectilinear triangle^ whose sides are equal in length to thote of the proposed sfiherical triangle*. Scholium. We have already given, at th. 5 chap, iv, expressions...

...proposed, of which the sides are very small, compared frith 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 to diminished may be taken for the angles of a rectilinear triangle, whose sides are equal in length...

...proposed, of which the sides are very small, compared with the radius of ike 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 anglet so diminished may be taken for the angles of a rectilinear triangle, whose sides are equal in...

...the 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...be taken for the angles of a rectilinear triangle, the sides of which are equal in length to those of the proposed spherical triangle'1 The demonstration...

....— - --^ -• . • *r /.-••" * ' f • » «,<,-» OJ itianelesone third of the excess o/Jhe sum of its three angles above two right angles be subtracted, the angles so dim? nifhedmay be taken for the angles *f" rectilinear triangle, whose side are equal M length to those-of...

...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...

...iti angles we subtract a third of the excess of the sum of the three angles aver two ri^ht 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...