## A Treatise on Practical Surveying: Which is Demonstrated from Its First Principles. Wherein Everything that is Useful and Curious in that Art, is Fully Considered and Explained |

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Página 54

Let DHB be a quadrant of a circle described by the radius CB ; BH an arc of it , and DH its complement ; HL or FC the sine , FH or CL its

Let DHB be a quadrant of a circle described by the radius CB ; BH an arc of it , and DH its complement ; HL or FC the sine , FH or CL its

**co**- sine ; BK its tangent DI its**co**- tangent ; CK its**secant**, and CI its**co**-**secant**. fig . Página 55

6. The

6. The

**co**- sine of an arc is to radius , as radius is to the**secant**. 7. The sine of an arc is to radius , as the tangent is to the**secant**. The triangles CLH and CBK , being similar , ( by theo . 16. ) 1. OL : LH :: CB : BK . 2. Página 87

We will now shew how any sine , tangent , or

We will now shew how any sine , tangent , or

**secant**may be had , though the figures in the tables were defaced , mis - printed , or obliterated . PROB . I. To find the tangent which is defaced , by the sine and**co**- sine . Página 89

To find the

To find the

**secant**by the help of a**co**- sine ; which may be found of great use when a table of sines and tangents can only be had . From twice the radius , which is 20.00000 , take the**Co**- sine ... Página 90

From the double radius , Take the

From the double radius , Take the

**co**- sine of 57 ° . 20 ' 20.00000 9.73219 The rem . is the**secant**of 570. 20 ' req . 10.26781 5. To find a**secant**by the help of the sine and tangent . From the tangent added to radius , take the sine ...### Comentarios de la gente - Escribir un comentario

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### Términos y frases comunes

acres angle Answer base bearing called centre chains chord circle Co-sine Co-tang column contained decimal Deg Dist difference direct Dist distance divided division double draw drawn east edge equal EXAMPLE feet field field-book figures foot four four-pole give given greater ground half height Hence inches laid land length less logarithm manner measure meridian distance method multiplied needle object observe off-sets opposite parallel parallelogram perches perpendicular plane pole PROB proceed proportion quantity quotient radius reduce remainder right angles right line root scale secant sect side sights sine square station stationary suppose survey taken tangent theo THEOREM third triangle triangle ABC true turn variation whole

### Pasajes populares

Página 44 - 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 101 - ... on a side, denotes its length to be given in feet, yards, perches, or miles, &c. and this mark", either in an angle or on a side, denotes the angle or side to be required. ; From these proportions it may be observed ; that to find a side, when the angles and one side are given, any side may be made the radius; and to find an angle, one of the given sides must be made the radius. So that in the 1st, 2d, and 3d cases, any side as well required as given may be made the radius, and in the first statings...

Página 48 - Triangles upon equal bases, and between the same parallels, are equal to one another.

Página 95 - 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 116 - C' (89) (90) (91) (92) (93) 112. In any plane triangle, the sum of any two sides is to their difference as the tangent of half the sum of the opposite angles is to the tangent of half their difference.

Página 6 - POMEROY, of the said District, hath deposited in this Office the title of a Book, the right whereof he claims as Proprietor, in the words following, to wit : . . "Biography of the Signers to the Declaration of Independence.

Página 50 - 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 117 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.

Página 177 - ... the two cardinal points of your compass the point of the needle lies between (the north, south, east, and west being called the four cardinal points, and are graved on the bottom of the box), putting down those points together by their initial letters, and thereto annexing the number of degrees, counting from the north or south, as before, thus ; if the point of your needle lies between the north and east, north and west, south and east, or south and west points in the bottom of the box, then...

Página 286 - But if one corner cannot be seen from the other, run the line according to the given bearing, and observe the nearest distance between the line so run and the corner: then...