A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ...Lewis Nichols, 1806 - 452 páginas |
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Página 25
... chord is a right line drawn from one end of an arc or arch ( that is , any part of the circum- ference of a circle ) ... chord : thus the space which is comprehended between the chord HG D Plate 1 . and the arc HBG , or that GEOMETRY . 25.
... chord is a right line drawn from one end of an arc or arch ( that is , any part of the circum- ference of a circle ) ... chord : thus the space which is comprehended between the chord HG D Plate 1 . and the arc HBG , or that GEOMETRY . 25.
Página 26
... chord HG and the arc HDAEG are called segments . Whence ' tis plain , fig . 8 . 1. That any chord will divide the circle into two segments . 2. The less the chord is , the more unequal are the segments . 3. When the chord is greatest it ...
... chord HG and the arc HDAEG are called segments . Whence ' tis plain , fig . 8 . 1. That any chord will divide the circle into two segments . 2. The less the chord is , the more unequal are the segments . 3. When the chord is greatest it ...
Página 39
... a circle which stands on the same chord as AB , are equal to each other , for they are all measured by half the arc they stand on . viz . by half the arc AB . fig . 26 . Plate I. Cor . 3. Hence an angle in a THEOREMS . 39.
... a circle which stands on the same chord as AB , are equal to each other , for they are all measured by half the arc they stand on . viz . by half the arc AB . fig . 26 . Plate I. Cor . 3. Hence an angle in a THEOREMS . 39.
Página 40
... chord AB , it will bisect it in the point D. fig . 29 . Let the lines AC and AB be drawn from the centre to the extremities of the chord , then since CA = CB , the angles CAB = CBA ( by the lem- ma . ) But the triangles ADC , BDC are ...
... chord AB , it will bisect it in the point D. fig . 29 . Let the lines AC and AB be drawn from the centre to the extremities of the chord , then since CA = CB , the angles CAB = CBA ( by the lem- ma . ) But the triangles ADC , BDC are ...
Página 41
... chord , bisects that chord at right angles ; therefore , con- versely , a line bisecting a chord at right angles must pass through the centre , and consequently be a diameter . THEOREM IX . If from the centre of a circle ABE there be ...
... chord , bisects that chord at right angles ; therefore , con- versely , a line bisecting a chord at right angles must pass through the centre , and consequently be a diameter . THEOREM IX . If from the centre of a circle ABE there be ...
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Términos y frases comunes
40 perches ABCD acres altitude Answer base bearing blank line centre chains and links chord circle circumferentor Co-sec Co-sine Co-tang Tang column contained cyphers decimal decimal fraction diameter difference distance line divided divisor draw drawn east edge EXAMPLE feet field-book figures fore four-pole chains half the sum height hypothenuse inches instrument Lat Dep Lat latitude line of numbers logarithm measure meridian distance multiplied needle number of degrees off-sets parallel parallelogram perpendicular piece of ground plane Plate prob PROBLEM proportion protractor quotient radius right angles right line scale of equal SCHOLIUM Secant second station sect semicircle side sights sine square root stationary distance sun's suppose survey taken tance tangent thence theo theodolite THEOREM trapezium triangle ABC trigonometry true amplitude two-pole chains vane variation whence
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.