# 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 SECTION III 23 Properties of Triangles 27 Square on the hypothenuse equal to the sum of 35 Of the Circle 47 Pyramid 67 SECTION XI 73 PART II 87
 Measures of the round bodies 168 6063 170 18 186 PART IV 188 19 198 23 206 6566 207 Of Cisterns 212

 4047 96 Mensuration of Surfaces 117 48 127 The unit of length or linear unit 130 Of the circle 141 60 156
 31 216 SECTION VII 218 SECTION III 233 Wheel and axle 240 ity is known 251

### Popular passages

Page 35 - If two triangles have two angles and the included side of the one, equal to two angles and the included side of the other, each to each, the two triangles will be equal.
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 82 - A zone is a portion of the surface of a sphere, included between two parallel planes which form its bases.
Page 142 - From eight times the chord of half the arc, subtract the chord of the whole arc, and divide the remainder by 3, and the quotient will be the length of the arc, nearly.
Page 84 - The convex surface of a cylinder is equal to the circumference of its base multiplied by its altitude.
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 41 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.
Page 36 - The angles opposite the equal sides of an isosceles triangle are equal.
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.