1. THE term TRIGONOMETRY is compounded of two Greek words Toyovos a triangle, and uɛrgov measure, signifying literally the measurement of triangles. It has for its object to determine the unknown parts of a triangle when a sufficient number of parts are known.
By parts of a triangle are understood commonly the sides and angles, though trigonometry properly includes the measurement of the surface also.
There will accordingly be six parts of every triangle, namely the three sides and the three angles.
2. It has been proved, (Geom. *B. 1, Props. 5, 6, and 10,) that when two triangles have three parts, one of which is a side, in the one equal respectively to the corresponding parts in the other, the triangles are equal.
One part must be a side, because if the three angles only were equal respectively in the two triangles they would be but similar, (Geom. B. 4, Prop. 18,) that is alike in shape but not necessarily in size.
Since all triangles which have three parts equal, are by consequence equal, it is said that three given parts determine a triangle, that is with these three given parts but one triangle can be formed.
If any number of attempts be made to form a new triangle
*The Geometry to which we refer here and elsewhere in this work, is Davies' Legendre.