This section is from the book "The Tinman's Manual And Builder's And Mechanic's Handbook", by Isaac Ridler Butt. Also available from Amazon: The Tinman's Manual And Builder's And Mechanic's Handbook.

1. The complement of an angle is its defect from a right angle.

2. The supplement of an angle is its defect from two right angles.

3. The sine, tangent, and secant of an angle, are the cosine, cotangent, and cosecant of the complement of that angle.

4. The hypotenuse of a right-angled triangle being made radii, its sides become the sines of the opposite angles, or the cosines of the adjacent angles.

5. The three angles of every triangle are equal to two right angles: hence the oblique angles of a right-angled triangle arc each others complements.

G. The sum of the squares of the two given sides of a right-angled triangle is equal to the square of the hypotenuse.

7. The difference between the Squares of the hypotenuse and given side of a right-angled triangle is equal to the square of the required side.

8. The area of a triangle equals half the product of the base multiplied by the perpendicular height; or,

9.. The area of a triangle equals half the product of the two sides and the natural sine of the contained angle.

L0. The side of any regular polygon multiplied by its apothem or perpen dicular, and by the number of its sides, equals twice the area.

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