## 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 81

A line

south so many degrees east or west , according as the line

north and east or north and west , or between the south and east or south and

west .

A line

**running**due north and south is called a meri . dian line . ... east or west , orsouth so many degrees east or west , according as the line

**runs**between thenorth and east or north and west , or between the south and east or south and

west .

Page 155

EXAMPLES . AD . 1. Given the area of the triangle ABC , Fig . 88 , equal 650

square perches and the length of the base AB 40 perches ; it is required to cut off

290 perchés towards the angle A , by a'line

EXAMPLES . AD . 1. Given the area of the triangle ABC , Fig . 88 , equal 650

square perches and the length of the base AB 40 perches ; it is required to cut off

290 perchés towards the angle A , by a'line

**running**from the angle C to the base . Page 165

S. 14 ° 45 ' E. to cut off 8 acres by a line

distance on the first side . Ans . 2.67 ch . 3. Given as follow ; 1st side , N. 74 ° 45 '

W , 2nd . N. 37 ° E. dist . 17.24 ch . Brd . N. 84o E. , to cut off a field containing 20

...

S. 14 ° 45 ' E. to cut off 8 acres by a line

**running**N. 87 ° 30 ' W .; required thedistance on the first side . Ans . 2.67 ch . 3. Given as follow ; 1st side , N. 74 ° 45 '

W , 2nd . N. 37 ° E. dist . 17.24 ch . Brd . N. 84o E. , to cut off a field containing 20

...

Page 167

14.40 ch . , and EF , S. 86 ° 00 ' E. to cut off a trapezium AEHI containing 82.3 sq .

ch . by a line HI

the distance AI = 3.51 ch . 2. Given as follow ; 1st side , N. 62 ° 15 ' W. 2nd .

14.40 ch . , and EF , S. 86 ° 00 ' E. to cut off a trapezium AEHI containing 82.3 sq .

ch . by a line HI

**running**S. 32 ° 15 ' W. Hence by the preceding problem we findthe distance AI = 3.51 ch . 2. Given as follow ; 1st side , N. 62 ° 15 ' W. 2nd .

Page 196

But , if one corner cannot be seen from the other ,

given bearing , and measure the ... 20 ch . and in

bearing , the corner is found 20 links to the left hand ; what allowance must be

made ...

But , if one corner cannot be seen from the other ,

**run**the line according to thegiven bearing , and measure the ... 20 ch . and in

**running**this line by the givenbearing , the corner is found 20 links to the left hand ; what allowance must be

made ...

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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.