## A System of Geometry and Trigonometry: Together with a Treatise on Surveying; Teaching Various Ways of Taking the Survey of a Field; Also to Protract the Same and Find the Area. Likewise, Rectangular Surveying; Or, an Accurate Method of Calculating the Area of Any Field Arithmetically, Without the Necessity of Plotting It. To the Whole are Added Several Mathematical Tables ... with a Particular Explanation ... and the Manner of Using Them ... |

### From inside the book

Page 11

The Tangent of an Arch of 45

The Tangent of an Arch of 45

**Degrees is equal in length to the Radius of the Circle of which the Arch is a part**. 24. The Secant of an Arch is a Line drawn from the Centre through one end of the Arch till it meets the Tangent ; thus CK ...### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Other editions - View all

SYSTEM OF GEOMETRY & TRIGONOME Abel 1765-1825 Flint,George Gillet,Frederick a. P. (Frederick Augu Barnard No preview available - 2016 |

SYSTEM OF GEOMETRY & TRIGONOME Abel 1765-1825 Flint,George Gillet,Frederick a. P. (Frederick Augu Barnard No preview available - 2016 |

### Common terms and phrases

according accurately added Angle Arch Base Bearing calculated called Chains Circle Co-Sine Sine Compass contained Course Decimals describe Diagonal Difference directions Dist Distance divided double draw drawn Elongation equal EXAMPLE Field FIELD BOOK Figure find the Angle find the Area four fourth give given greater half hand Hypothenuse Land Left Leg BC length less Line Links Logarithms manner measuring method Minutes multiply Natural Sines Needle North Note number of Degrees observe opposite parallel particular Perpendicular PLATE Plot Point practice preceding PROBLEM Product Proportion protract Quotient Radius Remainder represent Right Angled Rule Secant Co-Secant seen Side Sine Co-Sine Sine Sine Sine South Areas Square Square Root Star Station subtract Surveying Surveyor Table Tang Tangent Co-Secant Secant third Trapezoid Triangle TRIGONOMETRY true whole

### Popular passages

Page 28 - As the base or sum of the segments Is to the sum of the other two sides, So is the difference of those sides To the difference of the segments of the base.

Page 27 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Page 6 - The Circumference of every circle is supposed to be divided into 360 equal parts, called Degrees ; and each degree into 60 Minutes, each minute into 60 Seconds, and so on.

Page 24 - In this case the" hypothenuse may be found by the square root without finding the angles ; according to the following PROPOSITION. IN EVERY RIGHT ANGLED TRIANGLE, THE SUM OF THE SQUARES OF THE TWO LEGS IS EQUAL TO THE SQUARE OF THE HYPOTHENUSE. In the above EXAMPLE, the square of AB 78.7 is 6193.69, the square of BC 89 is 7921 ; these added make 14114,69 the square root of which is nearest 119.

Page 40 - Field work and protraction are truly taken and performed ; if not, an error must have been committed in one of them : In such cases make a second protraction ; if this agrees with the former, it is to be presumed the fault is in the Field work ; a re-survey must then be taken.

Page 33 - To find the area of a trapezoid. RULE. Multiply half the sum of the two parallel sides by the perpendicular distance between them : the product will be the area.

Page 6 - Therefore all radii of the same circle are equal. 13. The diameter of a circle is a right line drawn from one side of the circumference to the other, passing through the centre ; and it divides the circle into two equal parts, called semicircles ; as AB or DE.

Page 40 - Let his attention first be directed to the map, and inform him that the top is north, the bottom south, the right hand east, and the left hand west.

Page 23 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.