The new practical builder, and workman's companion, Volum 2

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Thomas Kelly, 1823
 

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Side 27 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Side 20 - The areas of two triangles which have an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Side 51 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.
Side 15 - AXIOMS. 1. Things which are equal to the same thing are equal to one another. 2. If equals be added to equals, the wholes are equal. 3. If equals be taken from equals, the remainders are equal.
Side 15 - LET it be granted that a straight line may be drawn from any one point to any other point.
Side 28 - ... angles of another, the third angles will also be equal, and the two triangles will be mutually equiangular. Cor.
Side 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Side 80 - The sine of an arc is a straight line drawn from one extremity of the arc perpendicular to the radius passing through the other extremity. The tangent of an arc is a straight line touching the arc at one extremity, and limited by the radius produced through the other extremity.
Side 28 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Side 22 - The perpendicular is the shortest line that can be drawn from a point to a straight line.

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