## The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying |

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The Principles of Plane Trigonometry, Mensuration, Navigation and Surveying ... Jeremiah Day No preview available - 2016 |

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added angled triangle arithmetical base calculation called chord circle circumference common complement contains cosine course departure determined diameter Diff difference of latitude direction distance divided draw drawn earth east equal equator Example extend feet field figure frustum give given greater half height hypothenuse inches increase length less logarithm longitude manner measured meridian method middle miles minutes multiplied nearly negative NOTE object observed obtained opposite parallel passes perpendicular plane pole polygon PROBLEM proportion pyramid quadrant quantity radius regular remaining right angled rods root rule sailing scale secant segment ship sides similar sine solidity sphere square stations subtract surface survey tables taken taking tangent term theorem third triangle trigonometrical true whole

### Popular passages

Page 78 - 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 29 - 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 36 - The surface of a sphere is equal to the product of its diameter by the circumference of a great circle.

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 54 - ADB, (Fig. 6.) be an arc, of which AB is the chord, . BF the sine, and AF the versed sine. The angle ABH is a right angle, (Euc. 31. 3.) and the triangles ABH, and ABF, are similar.

Page 17 - CUBIC MEASURE 1728 cubic inches = 1 cubic foot 27 cubic feet = 1 cubic yard...

Page 9 - 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 7 - Or, multiply the whole diameter into the whole circumference, and take i of the product. The area of a circle is equal to the product of half the diameter into half the circumference; (Sup. Euc. 5, 1.) or which is the same thing, { the product of the diameter and circumference.

Page 2 - 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 92 - 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.