# Elements of Geometry and Trigonometry: With Applications in Mensuration

A.S. Barnes & Company, 1870 - Geometry - 319 pages

### Contents

 DEFINITIONS and Remarks 9 Axioms 16 BOOK II 38 Problems relating to the First and Second Books 53 BOOK III 69 BOOK IV 82 Measurement of Areas and Proportions of Figures 109
 BOOK V 116 BOOK VI 126 Appendix 163 OF LOGARITHMS 165176 165 APPLICATIONS OF GEOMETRY 211 MENSURATION OF SOLIDS 239 MENSURATION OF THE ROUND BODIES 248

### Popular passages

Page 48 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Page 12 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, etc.
Page 25 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.
Page 85 - 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 208 - To find the area of a trapezoid. RULE. Multiply the sum of the parallel sides by the perpendicular distance between them, and then divide the product by two : the quotient will be the area (Bk.
Page 41 - In the lower numbers the maps avoid unnecessary detail, while respectively progressive, and affording the pupil new matter for acquisition each time he approaches in the constantly enlarging circle the point of coincidence with previous lessons in the more elementary books.
Page 169 - In every plane triangle there are six parts : three sides and three angles. These parts are so related to each other, that when one side and any two other parts are given, the remaining ones can be obtained, either by geometrical construction or by trigonometrical computation.
Page 197 - Being on a horizontal plane, and wanting to ascertain the height of a tower, standing on the top of an inaccessible hill, there were measured, the angle of elevation of the top of the hill 40°, and of the top of the tower 51° ; then measuring in a direct line 180 feet farther from the hill, the angle of elevation of the top of the tower Cway 33° 45' ; required the height of the tower.
Page 79 - If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts.
Page 119 - If a cone be cut by a plane parallel to the base, the section will be a circle.