The Theory and Practice of Surveying: Containing All the Instructions Requisite for the Skillful Practice of this ArtE. Duyckinck, 1821 - 544 σελίδες |
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Σελίδα 53
... Whence if any numbers of right lines were drawn from one point , on the same side of a right line ; all the angles made by these lines will be equal to two right angles . 2. And all the angles which can be made about a point , will be ...
... Whence if any numbers of right lines were drawn from one point , on the same side of a right line ; all the angles made by these lines will be equal to two right angles . 2. And all the angles which can be made about a point , will be ...
Σελίδα 59
... whence the arc AF = FB , and so AFB is bisected in F , by the line CF of an arc is half the For AD is the sine of AF is half the arc , and Cor . Hence the sine chord of twice that arc . the arc AF , ( by def . 22. ) AD half the chord AB ...
... whence the arc AF = FB , and so AFB is bisected in F , by the line CF of an arc is half the For AD is the sine of AF is half the arc , and Cor . Hence the sine chord of twice that arc . the arc AF , ( by def . 22. ) AD half the chord AB ...
Σελίδα 60
... whence IK is not parallel , and the like we can prove of all other lines but AB ; there- fore AB is parallel to CD . Q. E. D. THEO . XII PL . 1. fig . 3 . If two equal and parallel lines AB , CD , be joined by two other lines AD , BC ...
... whence IK is not parallel , and the like we can prove of all other lines but AB ; there- fore AB is parallel to CD . Q. E. D. THEO . XII PL . 1. fig . 3 . If two equal and parallel lines AB , CD , be joined by two other lines AD , BC ...
Σελίδα 63
... whence the lines on any scale are formed , is the chord of 60 de- grees on the line of chords . THEO . XVI . PL . 1. fig . 34 . = If in two triangles ABC , abc , all the angles of one be each respec tively equal to all the angles of the ...
... whence the lines on any scale are formed , is the chord of 60 de- grees on the line of chords . THEO . XVI . PL . 1. fig . 34 . = If in two triangles ABC , abc , all the angles of one be each respec tively equal to all the angles of the ...
Σελίδα 65
... Whence also the parallelograms ABCF and BDEC , being ( by cor . 2. theo . 12. ) the doubles of the triangles , are likewise as their bases . Q.E.D. Note . Wherever there are several quantities connected with the sign ( : :) the ...
... Whence also the parallelograms ABCF and BDEC , being ( by cor . 2. theo . 12. ) the doubles of the triangles , are likewise as their bases . Q.E.D. Note . Wherever there are several quantities connected with the sign ( : :) the ...
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ABCD acres altitude Answer arch base bearing centre chains and links circle circumferentor Co-sec Co-tang column compasses contained cube root decimal diagonal difference of latitude Dist divided divisions divisor draw east Ecliptic edge EXAMPLE feet field-book figure four-pole chains geometrical series given angle given number half the sum height Hence Horizon glass hypothenuse inches instrument length Logarithms measure meridian distance multiplied Natural Co-sines natural number natural sine Nonius number of degrees object observed off-sets opposite parallelogram perches perpendicular plane pole PROB proportional protractor Quadrant quotient radius rhombus right angles right line screw Secant sect semicircle side square root station subtract survey taken tance Tang tangent theo theodolite trapezium triangle ABC trigonometry two-pole chains vane versed sine vulgar fraction whence
Δημοφιλή αποσπάσματα
Σελίδα 246 - ... that triangles on the same base and between the same parallels are equal...
Σελίδα 58 - 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 231 - RULE. From half the sum of the three sides subtract each side severally.
Σελίδα 45 - 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 14 - Then multiply the second and third terms together, and divide the product by the first term: the quotient will be the fourth term, or answer.
Σελίδα 5 - His method is founded on these three considerations: 1st, that the sum of the logarithms of any two numbers is the logarithm of the product of...
Σελίδα 91 - ... scale. Given the length of the sine, tangent, or secant of any degrees, to find the length of the radius to that sine, tangent, or secant.
Σελίδα 35 - DIVISION BY LOGARITHMS. RULE. From the logarithm of the dividend subtract the logarithm of the divisor, and the number answering to the remainder will be the quotient required.
Σελίδα 30 - Then, because the sum of the logarithms of numbers, gives the logarithm of their product ; and the difference of the logarithms, gives the logarithm of the quotient of the numbers ; from the above two logarithms, and the logarithm of 10, which is 1, we may obtain a great many logarithms, as in the following examples : EXAMPLE 3.
Σελίδα 211 - At 170 feet distance from the bottom of a tower, the angle of its elevation was found to be 52° 30' : required the altitude of the tower ? Ans.