...line AD 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...

...the 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...

...and С с ; draw P О perpendicular to Ce; and join OQ. Then, because the triangles С P с, С Q с have the three sides of the one equal to the three sides scribe two circles, and kt them cut one another in P; and from P draw PM perpendicular to А В : then...

...and, by transposition, A> B+ C— 360° + 180°, or A > (B + C) — 180°, as we wished to prove. 449. Theorem. If two spherical triangles on the same sphere, or on equal sphere?, are equilateral with respect to each other, they are also equiangular with respect to each...

...and, by transposition, A>^-B1C — 360° + 180°, or *9>(5+ C) — 180°, as we wished to prove. 449. Theorem. If two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other. Proof....

...by transposition, A > -f- BC — 360° + 180°, or A>(B + C)— 180°, as we wished to prove. 449. Theorem. If two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other. Proof....

...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCS, have the three sides of the one equal to the three sides of the Of the Circle. B other, each to each : viz. AC equal to CB, being radii, AD equal to DB, by hypothesis,...

...chord, and the arc AE equal to EB. First. Draw the two radii CA, CB. Then the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note. When reference is made from one theorem to another, in the same Book, the number of the theorem...

...chord, and the arc AE equal to EB- ^ First- Draw the two radii CA, CBThen the two triangles A CD, DCB, have the three sides of the one equal to the three sides of the *Note- When reference is made from one theorem to another, in the same Book, the number of the theorem...

...that similar prisms, or pyramids, are to each other as the cubes of their altitudes. 5. Prove that if two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other. LOGARITHMS...