A Treatise of Practical Surveying: Which is Demonstrated from Its First Principles ...Lewis Nichols, 1806 - 452 σελίδες |
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Σελίδα 26
... sine of an arc , is a perpendicular line let fall from one end thereof to a diameter drawn to the other end : thus HL is the right sine of the arc HB . The sines on the same diameter increase till they come to the centre , and so become ...
... sine of an arc , is a perpendicular line let fall from one end thereof to a diameter drawn to the other end : thus HL is the right sine of the arc HB . The sines on the same diameter increase till they come to the centre , and so become ...
Σελίδα 27
... sine of a quadrant becomes the sine of 90 degrees , or the fourth part of the circle , which is 360 de- grees . 23. The versed sine of an arc is that part of the diameter that lies between the right sine and the circumference : thus LB ...
... sine of a quadrant becomes the sine of 90 degrees , or the fourth part of the circle , which is 360 de- grees . 23. The versed sine of an arc is that part of the diameter that lies between the right sine and the circumference : thus LB ...
Σελίδα 28
... sine , tangent , or secant of the comple- ment of any arc , is called the co - sine , co - tangent , or co - secant of the arc itself : thus FH is the sine , DI the tangent , and CI the secant of the arc DH : or they are the co - sine ...
... sine , tangent , or secant of the comple- ment of any arc , is called the co - sine , co - tangent , or co - secant of the arc itself : thus FH is the sine , DI the tangent , and CI the secant of the arc DH : or they are the co - sine ...
Σελίδα 41
... sine of an arc is half the chord of 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 ...
... sine of an arc is half the chord of 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 ...
Σελίδα 42
... 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 . Q. E. D. THEOREM XI . If a right line GH cut two other right lines AB , CD , so as to make the alternate angles AEF , EFD ...
... 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 . Q. E. D. THEOREM XI . If a right line GH cut two other right lines AB , CD , so as to make the alternate angles AEF , EFD ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
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.