A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ...Lewis Nichols, 1806 - 452 σελίδες |
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Σελίδα 6
... plain trigonometry , right angled and oblique , with its application in determining the measures of inaccessible heights and distances . The third section gives an account of the chains and measures used in Great - Britain and Ireland ...
... plain trigonometry , right angled and oblique , with its application in determining the measures of inaccessible heights and distances . The third section gives an account of the chains and measures used in Great - Britain and Ireland ...
Σελίδα 26
... 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 becomes a di- ameter , and then the segments are equal ; and ...
... 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 becomes a di- ameter , and then the segments are equal ; and ...
Σελίδα 39
... plain ( by the preceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is double to CAD , and therefore ECD is double to CAD ; after the same manner ...
... plain ( by the preceding lemma ) that the angles subtended by them will be also equal , and that their sum is double to either of them , that is , DAC + ADC is double to CAD , and therefore ECD is double to CAD ; after the same manner ...
Σελίδα 41
... twice that arc . For AD is the sine of the arc AF , ( by def . 22. ) AF is half the arc , and AD half the chord AB ( by theo , 8. ) therefore the cor . is plain . F Plate I. THEOREM X. In any triangle ABD , the THEOREMS . 41.
... twice that arc . For AD is the sine of the arc AF , ( by def . 22. ) AF is half the arc , and AD half the chord AB ( by theo , 8. ) therefore the cor . is plain . F Plate I. THEOREM X. In any triangle ABD , the THEOREMS . 41.
Σελίδα 43
... plain , that the opposite sides of a parallelogram are equal ; for it has been proved that ABCD being a parallelogram , AB will be CD and AD = BC , THEOREM XIII . All parallelograms on the same or equal bases and between the same ...
... plain , that the opposite sides of a parallelogram are equal ; for it has been proved that ABCD being a parallelogram , AB will be CD and AD = BC , THEOREM XIII . All parallelograms on the same or equal bases and between the same ...
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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
Δημοφιλή αποσπάσματα
Σελίδα 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.
Σελίδα 207 - ... that triangles on the same base and between the same parallels are equal...
Σελίδα 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.
Σελίδα 43 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Σελίδα 103 - TO THEIR DIFFERENCE ; So IS THE TANGENT OF HALF THE SUM OF THE OPPOSITE ANGLES', To THE TANGENT OF HALF THEIR DIFFERENCE.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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°.
Σελίδα 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.