## A Treatise on Surveying, Containing the Theory and Practice: To which is Prefixed a Perspicuous System of Plane Trigonometry. The Whole Clearly Demonstrated and Illustrated by a Large Number of Appropriate Examples. Particularly Adapted to the Use of Schools |

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Page 102

To protract a

trapeziums . The method of doing this will be best understood by an example .

Thus , Suppose the following field - notes to be given , it is required to protract the

To protract a

**Survey**, and to find its area by dividing it into triangles andtrapeziums . The method of doing this will be best understood by an example .

Thus , Suppose the following field - notes to be given , it is required to protract the

**survey**... Page 103

To protract the

line ; then N standing for the north and S for the south , the east will be to the right

hand and the west to the left . In NS take any convenient point as A for the place ...

To protract the

**survey**. Method 1st . Draw NS , Fig . 75 , to represent a meridianline ; then N standing for the north and S for the south , the east will be to the right

hand and the west to the left . In NS take any convenient point as A for the place ...

Page 111

Half the difference of the sums of the numbers contained in these columns will be

the area of the

represent the boundary of a

the ...

Half the difference of the sums of the numbers contained in these columns will be

the area of the

**survey**. * DeMONSTRATION .-- Let ABCDEFGH , Fig . 78 ,represent the boundary of a

**survey**, and let NS be a meridian passing throughthe ...

Page 112

In a true

those of the east . ings and westings ; but ... If either of the errors exceed 2 links

for every 10 chains in the sum of the distances , a re -

but ...

In a true

**survey**the sum of the northings and southings will be equal , and alsothose of the east . ings and westings ; but ... If either of the errors exceed 2 links

for every 10 chains in the sum of the distances , a re -

**survey**ought to be taken ;but ...

Page 124

In taking a

going directly from the 3rd to the 4th corner by a pond of water . I therefore set up

two stakes near the edge of the pond , and took the bearing and distance from ...

In taking a

**survey**of a tract of land bounded by six straight sides , I was preventedgoing directly from the 3rd to the 4th corner by a pond of water . I therefore set up

two stakes near the edge of the pond , and took the bearing and distance from ...

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### Common terms and phrases

ABCD according acres adjacent angle base bearing bearing and distance Calculation called centre circle Co-secant Secant Co-sine Co-tang column Construction contained corresponding Courses decimal DegDegDeg DEMONSTRATION describe difference Dist distance divide division draw east equal EXAMPLES feet field figures find the area given given angle given area given side greater half hand height join latitude and departure length less logarithm measured meeting meridian distance Note Off-sets opposite parallel perches perpendicular preceding PROBLEM radius rectangle remainder Required the area right angled triangle right line root RULE running scale Secant side AC Sine square station subtract survey taken Tang Tangent tract of land triangle triangle ABC twice

### Popular passages

Page 2 - An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the times therein mentioned." And also to the act, entitled " An Act supplementary to an Act, entitled, " An Act for the encouragement of learning, by securing the copies of maps, charts, and books, to the authors and proprietors of such copies during the time therein mentioned," and extending the benefits thereof to the arts of designing, engraving, and...

Page 97 - To find the Area of a Triangle when the Three Sides are given. Rule. — From half the sum of the three sides subtract each side separately.

Page 43 - The angle at the centre of a circle is double of the angle at the circumference upon the same base, that is, upon the same part of the circumference.

Page 34 - 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 2 - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...

Page 85 - A maypole, whose top was broken off by a blast of wind, struck the ground at 15 feet distance from the foot of the pole: what was the height of the whole maypole, supposing the broken piece to measure 39 feet in length ? Ans.

Page 25 - A plane rectilineal angle is the inclination of two straight lines to one another, which meet together, but are not in the same straight line.

Page 26 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.

Page 91 - PROBLEM I. To find the area of a parallelogram; whether it be a square, a rectangle, a rhombus, or a rhomboides. RULE.* Multiply the length by the perpendicular height, and the product will be the area.

Page 96 - If one side and the angles are given ; then As the product of radius and the sine of the angle opposite the given side, To the product of the sines of the two other angles ; So is the square of the given side, To twice the area of the triangle. If PC (Fig.