...are equal to them, are equal to one another. (2l6.) COR. 2. Hence, if two spherical triangles have the three sides of the one equal to the three sides of the other, or two sides and the included angle in the one, equal to two sides and the included angle, in the other,...

...the other, coincide entirely ; thus two circles having the same radius arc equal ; and two triangles having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal...

...however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. .fc having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal...

...equivalent, however dissimilar ; thus a circle may be equivalent to a square, a triangle to a rectangle, &c. having the three sides of the one equal to the three sides of the other, each to each, are also equal. 162. Two figures are similar, which have the angles of the one equal...

...from the vertex A to the point D the middle of the base BC ; the two triangles ABD, ADC, will have the three sides of the one, equal to the three sides of the qther, each to each, namely, AD common to both, AB — AC, by hypothesis, and BD = DC, by construction...

...at right angles. OF GEOMETRY. Book I. s Sup. PROP. IV. THEOREM. If two triangles, ABC and DEF, have the three sides of the one equal to the three sides of the other, each to each, viif. AB to DE, AC to DF, and BC to EF, the triangles are equal in every respect. Let...

...parts ; they are not different, therefore, but equal; and \ve say, universally, When two triangles have the three sides of the one equal to the three sides of the other respectively, the angles will also be equal, respectively, and the two triangles will be equal in all...

...and the same great circle, meet in the poles of that circle. PROP. V. If two spherical triangles have the three sides of the one equal to the three sides of the other, each to each, the angles which are opposite to the equal sides are likewise equal ; and conversely....

...three angles of the one equal to the three angles of the other, each to each, they shall likewise have the three sides of the one equal to the three sides of the othrr, each to each, viz. those which are opposite to the equal angles.* Let the spherical triangles...

...describe (42.) the equilateral triangle BDC, and join A D. Then, because the triangles AB D, А С D have the three sides of the one equal to the three sides of the other, each to each, (7.) the angle BAD is equal to the angle CAD, Therefore, &c. Cer. By repeating this process...