## 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 |

### Dentro del libro

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Página 42

Hence the

Hence the

**sine**of an arc is half the chord of twice that arc . For AD is the**sine**of the arc AF and AF is half the arc , and AD half the chord AB ( by theo . 8. ) therefore the cor . is plain . Página 43

viz . the chord of BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE the half of BD is the

viz . the chord of BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE the half of BD is the

**sine**of BAD ; the same way may be proved , that half of AD is the**sine**of ABD , and the half of AB the**sine**of ADB . Página 47

Therefore , in general , the chord ,

Therefore , in general , the chord ,

**sine**, tangent , & c . of any arc is proportional to the radius of the circle ) the same way the chord AB is to the chord a b , in the same proportion . So AB : ab : THEOREMS . 47. Página 54

... or FC the

... 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 . 8 . gre . D IK F H А B C L 6 E 1. The co -**sine**of an arc is to the**sine**, as radius is to the tangent . Página 55

The

The

**sine**of an arc is to its co -**sine**, as radius to its co - tangent . 4. Or radius is to the co - tangent of an arc , as its**sine**to its co -**sine**. 5. The co - tangent of an arc is to radius , as radius * to the tangent . 6.### 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...