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

### Other editions - View all

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

### Common terms and phrases

ABCD altitude apparent level arithmetical complement axis base calculation circle circular segment circumference cosecant cosine cotangent course cylinder decimal departure and difference Diff difference of latitude difference of longitude distance divided earth equal equator feet field figure frustum gallons given side gles greater half height horizon hypothenuse inches JEREMIAH DAY length less logarithm measured Mercator's Merid meridian meridional difference miles minutes multiplied number of degrees number of sides object opposite parallelogram perimeter perpendicular plane sailing pole pole star polygon PROBLEM proportion pyramid quadrant quantity quotient radius ratio regular polygon right angled triangle right ascension rods root secant segment sine sines and cosines slant-height sphere spherical spirit level square stations subtract surface survey tables tangent term theorem trapezium triangle ABC Trig trigonometrical 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.