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

### Dentro del libro

Resultados 1-5 de 5

Página 40

Hence an angle in a segment greater than a semicircle is less than a right angle ;

thus ADB is measured by

semicircle , therefore

semicircle ...

Hence an angle in a segment greater than a semicircle is less than a right angle ;

thus ADB is measured by

**half**the arc AB , but as the arc AB is less than asemicircle , therefore

**half**the arc AB , or the angle ADB is less than**half**asemicircle ...

Página 103

Again EBC being

theo . 4. sect 1. ) also , since HB , HF , and the included angle H , are severally

equal to BC , CD , and the included angle BCD , therefore ( by theo . 6. sect . 1. )

...

Again EBC being

**half**HBC , will be also**half**the sum of the angles A and C ( bytheo . 4. sect 1. ) also , since HB , HF , and the included angle H , are severally

equal to BC , CD , and the included angle BCD , therefore ( by theo . 6. sect . 1. )

...

Página 105

Plate V. it is plain , that AC is the sum , and DB the difference of the two quantities

; and AE or EC , their

we add EB , we shall have AB , the greatest quantity ; and if from EC we take EB ...

Plate V. it is plain , that AC is the sum , and DB the difference of the two quantities

; and AE or EC , their

**half**sum , and DE or EB their**half**difference . Now if to AEwe add EB , we shall have AB , the greatest quantity ; and if from EC we take EB ...

Página 197

FA ~ HA CH , that is , the

between the

, and its root the area . Q. E. D. Hence the following problem will be evident .

FA ~ HA CH , that is , the

**half**sum multiplied continually into the differencesbetween the

**half**sum and each side , will be the square of the area of the triangle, and its root the area . Q. E. D. Hence the following problem will be evident .

Página 242

As before

trapezium bBCC ; after the same manner ,

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

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 , multipliedby cd , will give the area of the trapezium CDd ; and again ,

**half**the sum of Dd ,and ...

### Comentarios de la gente - Escribir un comentario

No encontramos ningún comentario en los lugares habituales.

### 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.