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

### Dentro del libro

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Página 19

A SQUARE number is the product of a number

number so

and 3 is the root of 9 , for 3

find its ...

A SQUARE number is the product of a number

**multiplied**by itself ; and thenumber so

**multiplied**, is called the root of that square ; thus 9 is the square of 3 ,and 3 is the root of 9 , for 3

**multiplied**by 3 is 9 . If a square number be given tofind its ...

Página 220

If the east meridian distances in the middle of each line be

particular southing , and the west meridian distances into the particular northing ,

the sum of these products will be the area of the map . Plate X. fig . 1 . Let the ...

If the east meridian distances in the middle of each line be

**multiplied**into theparticular southing , and the west meridian distances into the particular northing ,

the sum of these products will be the area of the map . Plate X. fig . 1 . Let the ...

Página 221

tances ef and hh ,

parallelograms are equal to the area of the map ; for if from them be taken the

four triangles marked Z , and in the place of those be substituted the four triangles

...

tances ef and hh ,

**multiplied**into the northings xg and ga ( my ) but these fourparallelograms are equal to the area of the map ; for if from them be taken the

four triangles marked Z , and in the place of those be substituted the four triangles

...

Página 222

... is made up of the meridian distance when east ,

and the meridian distance , when west ,

meridian distance , when west ,

.

... is made up of the meridian distance when east ,

**multiplied**into the southing ,and the meridian distance , when west ,

**multiplied**into the northing less by themeridian distance , when west ,

**multiplied**in the southing . Q. E. D. COROLLARY.

Página 242

As before half the sum of Bb , and Cc

trapezium bBCC ; after the same manner , half the sum of Cc , and Dd ,

by cd , will give the area of the trapezium CDd ; and again , half the sum of Dd ,

and ...

As before half the sum of Bb , and Cc

**multiplied**by bc , will be the area of thetrapezium bBCC ; after the same manner , half the sum of Cc , and Dd ,

**multiplied**by cd , will give the area of the trapezium CDd ; and again , half the sum of Dd ,

and ...

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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.