First Lessons in Geometry: With Practical Applications in Mensuration, and Artificers' Work and Mechanics
A.S. Barnes, 1840 - Geometrical drawing - 252 pages
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14 feet ABCD acres altitude axis base bounded breadth called centre chains chord circle circumference cone construction contain convex surface cubic feet cylinder decimal describe diameter dimensions distance divided divisions draw drawn equal EXAMPLES Explain the manner expressed faces fall feet 6 inches figure find the area foot Give given line given point greater half hand height Hence hexagon inches included inscribed intersect known length marked measure Mensuration of Surfaces multiplied opposite parallel parallelogram pass pentagon perpendicular piece plane polygon Practical Geometry prism PROBLEM pyramid radius rectangle regular Required the area right angles rods Round Bodies RULE ruler scale segment side similar solid specific gravity sphere square feet straight line taken tangent thickness third timber triangle unit zone
Page 20 - Every circumference of a. circle, whether the circle be large or small, is supposed to be divided into 360 equal parts called degrees. Each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds.
Page 32 - The area of a rectangle is equal to the product of its base and altitude. Given R a rectangle with base b and altitude a. To prove R = a X b. Proof. Let U be the unit of surface. .R axb U' Then 1x1 But - is the area of R.
Page 40 - Similar triangles are to each other as the squares described on their homologous sides. Let ABC, DEF be two similar triangles...
Page 80 - A zone is a portion of the surface of a sphere included between two parallel planes.
Page 233 - An equilibrium is produced in all the levers, when the weight multiplied by its distance from the fulcrum is equal to the product of the power multiplied by its distance from the fulcrum. That...
Page 82 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.
Page 34 - The area of a triangle is equal to half the product of the base and height.
Page 35 - If two triangles have two sides and the included angle of the one, equal to two sides and the included angle of the other, each to each, the two triangles will be equal in all their parts." Axiom 1. "Things which are equal to the same thing, are equal to each other.
Page 20 - For this purpose it is divided into 360 equal parts, called degrees, each degree is divided into 60 equal parts called minutes, and each minute into 60 equal parts called seconds. The degrees, minutes, and seconds, are marked thus, °, ', " ; and 9° 18' 10", are read, 9 degrees, 18 minutes, and 10 seconds.
Page 81 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.