## A Course of Mathematics: Containing the Principles of Plane Trigonometry, Mensuration, Navigation, and Surveying : Adapted to the Method of Instruction in the American Colleges |

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added angled triangle base calculation called chord circle circumference column common complement contains cosine course decimal departure determined diameter difference of latitude direction distance divided division draw drawn earth equal equator Example expressions extend feet field figure fourth frustum given greater half height hypothenuse inches increase latter length less logarithm longitude manner measured meridian method middle miles minutes multiplied natural nearly negative Note object observed opposite parallel perimeter perpendicular plane polygon portion positive PROBLEM proportion pyramid quadrant quantity radius ratio regular right angled rods root rule sailing scale secant segment ship sides similar sine solidity sphere square subtract supposed surface survey tables taken taking tangent term theorem third triangle trigonometry whole

### Popular passages

Page 51 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds.

Page 19 - 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 26 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.

Page 57 - ... the square of the hypothenuse is equal to the sum of the squares of the other two sides.

Page 47 - 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, and the area computed, the chain is found to be too long or too short ; the true contents may be found, upon the principle that similar figures are to each other as the squares of their homologous sides.

Page 7 - RULE. Find the area of the sector which has the same arc, and also the area of the triangle formed by the chord of the segment and the radii of the sector. Then...

Page 119 - 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. By Theorem II. we have a : b : : sin. A : sin. B.

Page 15 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...

Page 43 - GF : hence also, the sum of the eastings is equal to the sum of the westings. We therefore conclude, that when any survey is correctly made, the sum of the northings will be equal to the sum of the southings, and the sum of the eastings to the sum of the westings.