# A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying

Durrie and Peck, 1851 - Geometry

### Contents

 Different Systems of Logarithms 42 Computation of Logarithms 45 TRIGONOMETRY 49 Sines Tangents Secants 51 Solutions of Right angled Triangles 66 Solutions of Oblique angled Triangles 80 Geometrical Construction of Triangles 91 Description and use of Gunters Scale 97 Trigonometrical Analysis 105 Computation of the Canon 123 Particular Solutions of Triangles 127 Notes 137 Table of Natural Sines and Tangents Page 147 22 148 30 152 35 153
 91 68 97 71 APPENDIX PART I 72 105 73 PART II 80 123 82 127 83 Notes 86 86 147 94 HEIGHTS AND DISTANCES 1 Plane Sailing 15 SURVEYING 57 Tables 95 15 102 25 111 86 117

### Popular passages

Page 81 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.
Page 43 - A cone is a solid figure described by the revolution of a right angled triangle about one of the sides containing the right angle, which side remains fixed.
Page 118 - The sum of any two sides of a triangle is to their difference, as the tangent of half the sum of the angles opposite to those sides, to the tangent of half their difference.
Page 61 - When a quantity is greater than any other of the same class, it is called a maximum. A multitude of straight lines, of different lengths, may be drawn within a circle. But among them all, the diameter is a maximum. Of all sines of angles, which can be drawn in a circle, the sine of 90° is a maximum. When a quantity is less than any other of the same class, it is called a minimum. Thus, of all straight lines drawn from a given point to a given straight line, that which is perpendicular to the given...
Page 69 - This will reduce the whole to the triangle MGD, which is equal to the original figure. The area of the triangle may then be found by multiplying its base into half its height ; and this will be the contents of the field. In practice, it will not be necessary actually to draw the parallel lines BD, GC, &c. It will be sufficient to lay the edge of a rule on C, so as to be parallel to a line supposed to pass through B and D, and to mark the point of intersection G. 126. If after a field has been surveyed,...
Page 21 - THE AREA OF THE TRIANGLE FORMED BY THE CHORD OF THE SEGMENT AND THE RADII OF THE SECTOR. THEN, IF THE SEGMENT BE LESS THAN A SEMI-CIRCLE, SUBTRACT THE AREA OF THE TRIANGLE FROM THE AREA OF THE SECTOR.
Page 48 - PROBLEM VI. To find the SOLIDITY of a FRUSTUM of a cone. 68. ADD TOGETHER THE AREAS OF THE TWO ENDS, AND THE SQUARE ROOT OF THE PRODUCT OF THESE AREAS; AND MULTIPLY THE SUM BY 1 OF THE PERPENDICULAR HEIGHT.
Page 98 - For, by art. 14, the decimal part of the logarithm of any number is the same, as that of the number multiplied into 10, 100, &c.
Page 14 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another : 16. And this point is called the centre of the circle.
Page 56 - From the same demonstration it likewise follows that the arc which a body, uniformly revolving in a circle by means of a given centripetal force, describes in any time is a mean proportional between the diameter of the circle and the space which the same body falling by the same given force would descend through in the same given time.