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

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Página 28

The sine , tangent , or

, co - tangent , or co -

and CI the

The sine , tangent , or

**secant**of the complement of any arc , is called the co - sine, co - tangent , or co -

**secant**of the arc itself : thus FH is the sine , DI the tangent ,and CI the

**secant**of the arc DH : or they are the co - sine , co - tangent , or co ... Página 78

In which you may observe , that each page is divided into 3 columns , the first and

last of which are minutes , and the intermediate ones contain the sines , tangents

, and

In which you may observe , that each page is divided into 3 columns , the first and

last of which are minutes , and the intermediate ones contain the sines , tangents

, and

**secants**, the upper and lower columns contain degrees , the column of ... Página 81

To find the

when a table of sines and tangents can only be had . From twice the radius ,

which is 20.00000 , take the co - sine , and the remainder will be the

theo .

To find the

**secant**by the help of a co - sine ; which may be found of great usewhen a table of sines and tangents can only be had . From twice the radius ,

which is 20.00000 , take the co - sine , and the remainder will be the

**secant**, ( bytheo .

Página 82

To find a

radius , take the sine , the remainder will be the

EXAMPLE Required , the

To find a

**secant**by the help of the sine and tangent . From the tangent added toradius , take the sine , the remainder will be the

**secant**, ( by theo , 24. part 7. )EXAMPLE Required , the

**secant**of 57o . 20 by help of the sine and tangent . Página 84

Which is Demonstrated from Its First Principles ... Robert Gibson. Plate V. 2. If one

leg AB be made the radius , and with it , on the point A , an arc be described ;

then BC is the tangent , and AC is the

fig ...

Which is Demonstrated from Its First Principles ... Robert Gibson. Plate V. 2. If one

leg AB be made the radius , and with it , on the point A , an arc be described ;

then BC is the tangent , and AC is the

**secant**of the angle A , by def . 24 and 25.fig ...

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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.