# ELEMENTS OF GEOMETRY AND TRIGONOMETRY

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### Innhold

 INTRoduction 9 Propositions 21 Ratios and Proportions 47 The Circle and the Measurement of Angles 57 Problems relating to the First and Third Books 76 Proportions of FiguresMeasurement of Areas 87 Problems relating to the Fourth Book 122 B O O K 139
 Multiplication by Logarithms 261 Problems 267 Table of Natural Sines 273 Solution of Triangles 281 Solution of RightAngled Triangles 287 Circular Functions 297 of Formulas 306 Homogeneity of Terms 3 13 313

 BOOK 156 B O O K W II 167 Polyedrons 174 The Three Round Bodies 202 Spherical Geometry as 227 Note A 245 Logarithms Defined 255 AN AI YTIC AI PLANE TRIG ON O METRY 257
 Spherical Triangle Defined 321 Napiers Analogies 329 Of Quadrantal Triangles 335 Area or Contents of a Surface + 347 Area of a Regular Polygon 353 Mensuration of Solids divided into Two Parts 358 Convex Surface of a Cone 364

### Populære avsnitt

Side 24 - 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.
Side 38 - That, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, meet on that side on which are the angles less than the two right angles.
Side 227 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Side 271 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees...
Side 43 - Hence, the interior angles plus four right angles, is equal to twice as many right angles as the polygon has sides, and consequently, equal to the sum of the interior angles plus the sum of the exterior angles.
Side 215 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.
Side 107 - If two triangles have two angles of the one equal to two angles of the other, each to each, and also one side of the one equal to the corresponding side of the other, the triangles are congruent.
Side 93 - The area of a parallelogram is equal to the product of its base and altitude.
Side 231 - The angles of spherical triangles may be compared together, by means of the arcs of great circles described from their vertices as poles and included between their sides : hence it is easy to make an angle of this kind equal to a given angle.
Side 232 - F, be respectively poles of the sides BC, AC, AB. For, the point A being the pole of the arc EF, the distance AE is a 'quadrant ; the point C being the pole of the arc DE, the distance CE is likewise a quadrant : hence the point E is...