## A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ... |

### Dentro del libro

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Página 25

A

the circumference of a circle ) to the other ; and is the measure Thus the right line

HG , is the measure of the arc HBG . fig . 8 . 20. The segment of a circle is any

part ...

A

**chord**is a right line drawn from one end of an arc or arch ( that is , any part ofthe circumference of a circle ) to the other ; and is the measure Thus the right line

HG , is the measure of the arc HBG . fig . 8 . 20. The segment of a circle is any

part ...

Página 26

Plate 1 . and the arc HBG , or that which is comprehended between the said

That any

the ...

Plate 1 . and the arc HBG , or that which is comprehended between the said

**chord**HG and the arc HDAEG are called segments . Whence ' tis plain , fig . 8 . 1.That any

**chord**will divide the circle into two segments . 2. The less the**chord**is ,the ...

Página 41

Hence it follows , that any line bisecting a

a line drawn from the centre perpendicular to a

angles ; therefore , conversely , a line bisecting a

Hence it follows , that any line bisecting a

**chord**at right angles , is a diameter ; fora line drawn from the centre perpendicular to a

**chord**, bisects thạt**chord**at rightangles ; therefore , conversely , a line bisecting a

**chord**at right angles must ... Página 46

Hence the radius , from whence the lines on any scale are formed , is the

60 degrees on the line of

all the angles of one be each respectively equal to all the angles of the other ...

Hence the radius , from whence the lines on any scale are formed , is the

**chord**of60 degrees on the line of

**chords**. THEOREM XVI . If in two triangles ABC , abc ,all the angles of one be each respectively equal to all the angles of the other ...

Página 63

If the lines which include the angle , be not as , long as the

scale , produce them to that or a greater ... with the

the arc ed ; which distance e d , measured on the same line of

...

If the lines which include the angle , be not as , long as the

**chord**, of 60 on yourscale , produce them to that or a greater ... with the

**chord**of 60 from B , describethe arc ed ; which distance e d , measured on the same line of

**chords**, gives the...

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### Términos y frases comunes

acres angle Answer base bearing called centre chains chord circle Co-sec Co-sine Co-tang column contained decimal difference direct distance divided division draw drawn east edge equal EXAMPLE feet field field-book figures four four-pole fourth give given greater ground half height Hence inches laid land Lat Dep length less logarithm manner measure method multiplied needle object observe opposite parallel perches perpendicular plain plane Plate pole prob PROBLEM proportion quantity quotient radius reduce remainder right angles right line root scale Secant sect side sights sine square station suppose survey taken Tang tangent theo THEOREM third triangle triangle ABC true turn variation whence whole

### Pasajes populares

Página 25 - The circumference of every circle is supposed to be divided into 360 equal parts, called degrees ; and each degree into 60 equal parts, called minutes ; and each minute into 60 equal parts, called seconds ; and these into thirds, &c.

Página 207 - ... that triangles on the same base and between the same parallels are equal...

Página 40 - The angle in a semicircle is a right angle ; the angle in a segment greater than a semicircle is less than a right angle ; and the angle in a segment less than a semicircle is greater than a right angle.

Página 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Página 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Página 31 - Figures which consist of more than four sides are called polygons ; if the sides are all equal to each other, they are called regular polygons. They sometimes are named from the number of. their sides, as a five-sided figure is called a pentagon, one of six sides a hexagon, &"c.

Página 31 - ... they are called regular polygons. They sometimes are named from the number of their sides, as a five-sided figure is called a pentagon, one of. six sides a hexagon, &c. but if their sides are not equal to each other, then they are called irregular polygons, as an irregular pentagon, hexagon, &c.

Página 45 - The hypothenuse of a right-angled triangle may be found by having the other two sides ; thus, the square root of the sum of the squares of the base and perpendicular, will be the hypothenuse. Cor. 2. Having the hypothenuse and one side given to find the other; the square root of the difference of the squares of the hypothenuse and given side will be the required side.

Página 265 - As the length of the whole line, Is to 57.3 Degrees,* So is the said distance, To the difference of Variation required. EXAMPLE. Suppose it be required to run a line which some years ago bore N. 45°.

Página 32 - Things that are equal to one and the same thing are equal to one another." " If equals be added to equals, the wholes are equal." " If equals be taken from equals, the remainders are equal.