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

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Página 26

Whence ' tis

segments . 2. The less the chord is , the more unequal are the segments . 3.

When the chord is greatest it becomes a diameter , and then the segments are

equal ; and ...

Whence ' tis

**plain**, fig . 8 . 1. That any chord will divide the circle into twosegments . 2. The less the chord is , the more unequal are the segments . 3.

When the chord is greatest it becomes a diameter , and then the segments are

equal ; and ...

Página 103

It is then

BC ; and since HB = BC , and BE perp and BE perpendicular to HC , therefore HE

= EC ( by theo . 8. sect . 1 ; ) and since BA = BI , and BD and IG parallel to AC ...

It is then

**plain**that AH will be the sum , and HI the difference of the sides AB andBC ; and since HB = BC , and BE perp and BE perpendicular to HC , therefore HE

= EC ( by theo . 8. sect . 1 ; ) and since BA = BI , and BD and IG parallel to AC ...

Página 104

Produce BD , till BG = AB the lesser leg ; and on B as a centre , with the distance

BG or BA , describe a circle AGHF ; which will cut BD , and AD in the points H and

F ; then it is

Produce BD , till BG = AB the lesser leg ; and on B as a centre , with the distance

BG or BA , describe a circle AGHF ; which will cut BD , and AD in the points H and

F ; then it is

**plain**, that GD will be the sum , and HD the difference of the sides ... Página 141

In the same manner the rest may be chained up and down ; but in going down it

is

thence suspended , will mark the point where he is to stick his peg . The figure is

...

In the same manner the rest may be chained up and down ; but in going down it

is

**plain**the leader of the chain must hold up the end thereof , and the plummetthence suspended , will mark the point where he is to stick his peg . The figure is

...

Página 196

It is

the area of the triangle ; or that half the sum of the sides , viz . CH * FD = the

triangle ; wherefore the square of CH by the square of FD = FC X FA ~ HA CH ,

that is ...

It is

**plain**, by the foregoing problem , that * AB x DE , + į BC * DG + į AČ ~ FD =the area of the triangle ; or that half the sum of the sides , viz . CH * FD = the

triangle ; wherefore the square of CH by the square of FD = FC X FA ~ HA CH ,

that is ...

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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.