## The New Practical Builder and Workman's Companion, Containing a Full Display and Elucidation of the Most Recent and Skilful Methods Pursued by Architects and Artificers ... Including, Also, New Treatises on Geometry ..., a Summary of the Art of Building ..., an Extensive Glossary of the Technical Terms ..., and The Theory and Practice of the Five Orders, as Employed in Decorative Architecture |

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ABCD added altitude angle ABD arches axes axis axis major base bisect called centre chord circle circumference common cone consequently construction contains COROLLARY covering curve cutting cylinder describe diameter difference distance divide draw drawn edge ellipse Engraved equal equation extremity factors figure four GEOMETRY given greater groin half Hence intersection join less manner meet method middle multiplying Nicholson opposite sides ordinate parallel parallelogram passing perpendicular placed plane PLATE points polygon position practical PROBLEM produced proportionals quantity radius rectangle ribs right angles roof seat segment semi-circle sides similar square straight line suppose surface tangent THEOREM third timber transverse axis triangle ABC vault vertex vertical whole

### Popular passages

Page 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.

Page 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'.

Page 51 - The area of a parallelogram is equal to the product of its base and its height: A = bx h.

Page 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.

Page 15 - LET it be granted that a straight line may be drawn from any one point to any other point.

Page 28 - ... angles of another, the third angles will also be equal, and the two triangles will be mutually equiangular. Cor.

Page 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.

Page 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.

Page 28 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...

Page 22 - The perpendicular is the shortest line that can be drawn from a point to a straight line.