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

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Page 10

... and the second , ten times greater than the third .

... and the second , ten times greater than the third .

**Hence**it appears , that as the value and denomination of any figure or number of figures in common arithmetic is enlarged , and becomes ten or an hundred 10 DECIMAL FRACTIONS . Page 26

The sines on the same diameter increase till they come to the centre , and so become the radius :

The sines on the same diameter increase till they come to the centre , and so become the radius :

**hence**it is plain that the radius CD is the greatest possible sine , and thence is called the whole sine . Since the whole sine CD ( fig . Page 28

is measured by the arc HB , and is said to contain so many degrees as the arc HB does ; so if the arc HB is 60 degrees , the angle HCB is an angle of 60 degrees .

is measured by the arc HB , and is said to contain so many degrees as the arc HB does ; so if the arc HB is 60 degrees , the angle HCB is an angle of 60 degrees .

**Hence**angles ... Page 30

**Hence**all triangles between the same parallels have the same height , since all the perpendiculars are equal from the nature of parallels . 43. Any figure of four sides is called a quadrilateral figure . 44. Page 37

**Hence**, if one angle of a triangle be known , the sum of the other two is also known : for since the three angles of every triangle contain two right ones , or 180 degrees ...### What people are saying - Write a review

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### Common terms and phrases

acres angle Answer base bearing called centre chains chord circle Co-sec Co-sine Co-tang column contained decimal difference direct distance divided divisions 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 off-sets opposite parallel perches perpendicular plain plane Plate 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

### Popular passages

Page 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.

Page 207 - ... that triangles on the same base and between the same parallels are equal...

Page 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.

Page 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Page 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Page 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.

Page 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.

Page 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.

Page 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°.

Page 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.