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

### Dentro del libro

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Página 102

EFORE we proceed to the solution of the four cases of Oblique angular triangles ,

it is necessary to premise the following theorems . THEOREM I. Plate V. In any

plane triangle ABC , the sides are proportional to the sines of their

EFORE we proceed to the solution of the four cases of Oblique angular triangles ,

it is necessary to premise the following theorems . THEOREM I. Plate V. In any

plane triangle ABC , the sides are proportional to the sines of their

**opposite**... Página 122

The external angle CBD , of the triangle ABC ; is equal to the two internal

internal

the other ...

The external angle CBD , of the triangle ABC ; is equal to the two internal

**opposite**ones , A , and ACB : ( by theo . 4. sect . 1. ) wherefore if one of theinternal

**opposite**angles be taken from the external angle ; the remainder will bethe other ...

Página 166

The circumferentor box may be taken off . Direct the sights to the object at the

second station , and the degree cut by the

bearing of that line from the north , and the same that the circumferentor would

give .

The circumferentor box may be taken off . Direct the sights to the object at the

second station , and the degree cut by the

**opposite**end of the index will be thebearing of that line from the north , and the same that the circumferentor would

give .

Página 205

If the perpendicular of two triangles fall on one and the same base , it is

unnecessary to put down the base twice , but insert the second perpendicular

perpendicular ...

If the perpendicular of two triangles fall on one and the same base , it is

unnecessary to put down the base twice , but insert the second perpendicular

**opposite**to the number of the triangles in the table , and join it with the otherperpendicular ...

Página 234

angular points between 1 and 2 , and take the bearing and length of the

stationary line 1 , 2 , and insert them in your field - book : but in chaining from 1 to

2 , stop at d

distance ...

angular points between 1 and 2 , and take the bearing and length of the

stationary line 1 , 2 , and insert them in your field - book : but in chaining from 1 to

2 , stop at d

**opposite**the angular point a , and in your field - book insert thedistance ...

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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.