## 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 26

4 . 11 . An obtuse angle is that which is greater than a right angle , as ADE , Fig .

4 . 12 .

being produced ever so far both ways , do not meet , as AB , CD , Fig ...

4 . 11 . An obtuse angle is that which is greater than a right angle , as ADE , Fig .

4 . 12 .

**Parallel**straight lines are those which are in the same plane , and which ,being produced ever so far both ways , do not meet , as AB , CD , Fig ...

Page 27

21 . Acute and obtuse angled triangles are called oblique angled triangles . 22 .

Any plane figure bounded by four right lines , is called a quadrilateral . 23 . Any

quadrilateral , whose opposite sides are

...

21 . Acute and obtuse angled triangles are called oblique angled triangles . 22 .

Any plane figure bounded by four right lines , is called a quadrilateral . 23 . Any

quadrilateral , whose opposite sides are

**parallel**, is called a parallelogram , as D...

Page 30

PROBLEM V. Through a given point A to draw a right line AB ,

right line CD , Fig . 22 . From the point A to any point F , in the line CD , draw the

right line AF ; with F as a centre and distance FA , describe the arc AE , and with ...

PROBLEM V. Through a given point A to draw a right line AB ,

**parallel**to a givenright line CD , Fig . 22 . From the point A to any point F , in the line CD , draw the

right line AF ; with F as a centre and distance FA , describe the arc AE , and with ...

Page 32

PROBLEM XI . To divide a given right line AB into any number of equal parts , Fig

. 28 . Draw the indefinite right line AP , making an angle with AB , also draw BQ ,

PROBLEM XI . To divide a given right line AB into any number of equal parts , Fig

. 28 . Draw the indefinite right line AP , making an angle with AB , also draw BQ ,

**parallel**to AP , in each of which , take as many equal parts AM , MN , & c . Page 33

... and draw HL

G PROBLEM XIV . To find a fourth proportional to three given right lines , A , B

and C. L A Draw two right lines , DE , DF B containing any angle ; make DG C

equal ...

... and draw HL

**parallel**to it : then will CL be the third E proportional required . сG PROBLEM XIV . To find a fourth proportional to three given right lines , A , B

and C. L A Draw two right lines , DE , DF B containing any angle ; make DG C

equal ...

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### Common terms and phrases

acres adjustment angle assumed base bearings and distances Calculation called centre chains changed Co-secant Secant Co-sine Co-tang column Construction contained correction corresponding decimal DEMONSTRATION departure describe diff difference of latitude direction dist divide division line draw east equal EXAMPLES feet field figure give given greater ground half hand height Hence horizontal indicated join length less logarithm manner measured meeting meridian middle multiplier Note object observed obtained opposite parallel passing perches perpendicular plane plate position PROBLEM radius ratio remainder right angles right line RULE running scale screws side Sine square stake stand stations straight subtract surface survey taken Tangent telescope tract of land triangle triangle ABC vernier

### Popular passages

Page 33 - 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 42 - 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 77 - 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 23 - 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 118 - 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 125 - From half the sum of the three sides, subtract each side severally; multiply the half sum, and the three remainders together, and the square root of the product will be the area required. Example. — Required the area of a triangle, whose sides are 50, 40, and 30 feet. 50 + 40+30 ; — 60, half the sum of the three sides.

Page 26 - A diameter of a circle is a straight line drawn through the centre, and terminated both ways by the circumference.

Page 34 - Sine, or Right Sine, of an arc, is the line drawn from one extremity of the arc, perpendicular to the diameter which passes through the other extremity. Thus, BF is the sine of the arc AB, or of the supplemental arc BDE.

Page 24 - Parallel straight lines are such as are in the same plane, and which being produced ever so far both ways, do not meet.

Page 16 - BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.