# Elements of Geometry and Trigonometry: With Applications in Mensuration

A.S. Barnes, 1886 - 324 sider

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### Innhold

 Durinitions and Remarks 910 9 Axioms 16 BOOK II 41 Problems relating to the First and Second Books 53 68 53 Ratios and Proportions 6981 69 Measurement of Areas and Proportions of Figures 82108 82 Problems relating to the Fourth Book 109113 109
 AppendixRegular Polygons 113115 115 Of Solids 126162 126 Appendix 163164 163 Page 165 MENSURATION OF SURFACES 211 MENsum ATION of Solids 239 MENsur ATION OF THE Roºse BoDIEs 248

### Populære avsnitt

Side 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.
Side 60 - After remarking that the mathematician positively knows that the sum of the three angles of a triangle is equal to two right angles...
Side 84 - 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.
Side 130 - ... or 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...
Side 49 - The angle formed by a tangent and a chord is measured by half the intercepted arc.
Side 209 - 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 was 33° 45' ; required the height of the tower.
Side 30 - The perpendicular is the shortest straight line that can be drawn from a given point to a given straight line; and...
Side 70 - To express that the ratio of A to B is equal to the ratio of C to D, we write the quantities thus : A : B : : C : D; and read, A is to B as C to D.
Side 12 - For the purpose of measuring angles, the circumference is divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes; each minute into 60 equal parts, called seconds.
Side 59 - 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.