SPHERICAL TRIGONOMETRY. T PROP. V. HE angles at the base of an isosceles spherical triangle are symmetrical magnitudes, not admitting of being laid on one another, nor of coinciding, notwithstanding their equality. It might be considered as a sufficient proof that they are equal, to observe that they are each determined to be of a certain magnitude rather than any other, by conditions which are precisely the same, so that there is no reason why one of them should be greater than another. For the sake of those to whom this reasoning may not prove satisfactory, the demonstration in the text is given, which is strictly geometrical. For the demonstrations of the two propositions that are given in the end of the Appendix to the Spherical Trigonometry, see Elementa Sphæricorum, Theor. 66. apud Wolfii Opera Math. tom. iii; Trigonometrie par Cagnoli, § 463; Trigonometrie Spherique par Mauduit § 165. FINIS. |