# Elementary Geometry: With Applications in Mensuration

A. S. Barnes & Company, 1850 - Geometry - 216 pages

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### Contents

 BOOK 9 Axioms 16 BOOK II 38 Problems relating to the First and Second Books 5368 53 BOOK III 69 BOOK IV 82 Problems relating to the Fourth Book 109113 109
 BOOK V 116 BOOK VI 126 Appendix 163164 163 Page 165 Mensuration of Solids 193 193 Mensuration of the Round Bodies 202

### Popular passages

Page 60 - 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 - 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 are equal in all respects.
Page 12 - For this purpose it is divided into 360 equal parts called degrees, each degree 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' 16", are read, 9 degrees 18 minutes and 16 seconds.
Page 70 - BD then A is said to have the same ratio to B, that C has to D ; or, the ratio of A to B is equal to the ratio of C to D.
Page 24 - America, but know that we are alive, that two and two make four, and that the sum of any two sides of a triangle is greater than the third side.
Page 130 - ... cylinder be cut by a plane parallel to the base, the section is a figure parallel and similar to the base. The one point a...
Page 124 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Page 174 - 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 161 - This pulyedrun may be considered as formed of pyramids, each having for its vertex the centre of the sphere, and for its base one of the faces of the polyedron.
Page 131 - If a cone be cut by a plane parallel to the base, the section will be a circle.