# 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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### Contents

 SECTION 15 Properties of Triangles 27 Properties of Polygons 40 SECTION IX 60 PART II 81 Dscription of Dividers and use 8788 87 PART III 117
 Of the circle 139153 141 Measures of the round bodies 168 PART IV 188 Of Cisterns 212 SECTION VII 218 SECTION III 233 Wheel and axle 240

### Popular passages

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 82 - A zone is a portion of the surface of a sphere included between two parallel planes.
Page 235 - 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 84 - 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 83 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.