...Mr. Ougktrtd, in his Trigonor metry. AXIOM I. As the Sine of half the Sum of two Sides' To the Sine of half their Difference ; So is the Co-tangent of...half the contained Angle, To the Tangent of half the Difference of the other Angles. Again : As the Co-fine of half the S_um of the Sides, To the Co-fine...

...II. As the Co-fine of half the Sum of the Sides, is ro the Co-fine of half their .Difference ; rfo lo is the Co-tangent of half the contained Angle, to the Tangent of half the Sum of the other two Angles. PROPOSITION III. As the Sine of half the Sum of the two Angles, is to the Sine of...

...• % P pp 2 As As the Sine of half the Sum of two Sides, to the fine of half their difference ; fo is the Co-tangent of half the contained Angle, to the Tangent of half the difference of the other Angles. Again, A? the Co-fine of half the fum of the fides, to the Co-fine...

...(containing an Angle) is to the Sine Complement of Half their Difference ; So is the Tangent Complement of half the contained Angle, to the Tangent of half the Sum of the other two Angles. Axiom 3. Firjt, As the Sine of half the Sum of two Angles ; is to the Sine of half...

...supplement of the required angle. THEOREM V. As the cosine of half the sum of two sides Is to the cosine of half their difference, So is the cotangent of half...contained angle To the tangent of half the sum of the other angle*. THEOREM VI. As the sine of half the sum of two angles Is to the sine of half their difference,...

...of the other angles ; and again, 2. As the cosine of half the sum of the two sides is to the cosine of half their difference, so is the cotangent of half...contained angle to the tangent of half the sum of the other two angles. And half the difference thus found added to half the sum gives the greater angle...