## 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 12

If the given number consist of five or six figures , find the logarithm of the four left

hand figures as before ; then take the difference between this logarithm and the

next

...

If the given number consist of five or six figures , find the logarithm of the four left

hand figures as before ; then take the difference between this logarithm and the

next

**greater**in the table . Multiply this difference by the remaining figure or figures...

Page 14

... the decimal part of the given logarithm , and if it cannot be found exactly , take

the one nearest to it , whether

column , marked No. which are in a line with the logarithm found , together with

the ...

... the decimal part of the given logarithm , and if it cannot be found exactly , take

the one nearest to it , whether

**greater**or less ; then the three figures in the firstcolumn , marked No. which are in a line with the logarithm found , together with

the ...

Page 52

This half difference of the two unknowo angles , added to their half sum , will give

the angle opposite the

the half sum , will give the angle opposite the less , given side . After finding the ...

This half difference of the two unknowo angles , added to their half sum , will give

the angle opposite the

**greater**of the two given sides , and being subtracted fromthe half sum , will give the angle opposite the less , given side . After finding the ...

Page 150

As the less number of the given ratio , Is to the

fourth term . * The square root of this fourth term will be the length required .

Having the length , the breadth may be found by the preceding problem . Or it

may ...

As the less number of the given ratio , Is to the

**greater**; So is the given area , To afourth term . * The square root of this fourth term will be the length required .

Having the length , the breadth may be found by the preceding problem . Or it

may ...

Page 178

Then , As the sum of the numbers expressing the ratio of the parts , Is to the

DC ; So is the rectangle of AD and sum of GD and GA , To a fourth term . Subtract

this ...

Then , As the sum of the numbers expressing the ratio of the parts , Is to the

**greater**or less of them , according as the**greater**or less part is to be adjacent toDC ; So is the rectangle of AD and sum of GD and GA , To a fourth term . Subtract

this ...

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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.