The Theory and Practice of Surveying: Containing All the Instructions Requisite for the Skilful Practice of this ArtEvert Duyckinck, 1814 - 508 σελίδες |
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Σελίδα 52
... measured by half the arc AB , but as the arc AB is less than a semicircle , therefore half the arc AB , or the angle ADB ... measure of the angle ABD , is half of a semicircle AED , and therefore a right angle . THEO . VIII . PL . 1. fig ...
... measured by half the arc AB , but as the arc AB is less than a semicircle , therefore half the arc AB , or the angle ADB ... measure of the angle ABD , is half of a semicircle AED , and therefore a right angle . THEO . VIII . PL . 1. fig ...
Σελίδα 53
... measure them ( by def . 19. ) : 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 Cor . Hence the sine chord of twice that arc . the arc AF , ( by def . 22. ) AF is half the ...
... measure them ( by def . 19. ) : 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 Cor . Hence the sine chord of twice that arc . the arc AF , ( by def . 22. ) AF is half the ...
Σελίδα 54
... measured by half the arc BKD , ( by cor 1 theo . 7. ) 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 ...
... measured by half the arc BKD , ( by cor 1 theo . 7. ) 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 ...
Σελίδα 57
... measured by the arc AEB ; therefore the sum of the other two angles is 120 degrees ( by Cor . 1. theo . 5. ) but since AC - CB , the angle CAB = CBA ( by lemma preceding theo . 7. ) con- sequently each of them will be 60 , the half of ...
... measured by the arc AEB ; therefore the sum of the other two angles is 120 degrees ( by Cor . 1. theo . 5. ) but since AC - CB , the angle CAB = CBA ( by lemma preceding theo . 7. ) con- sequently each of them will be 60 , the half of ...
Σελίδα 58
... measure BD : suppose that to be Ag , which will be contained twice in AB , and three times in BD , the parts Ag , gB , Bh , hi , and i D being all equal , and let the lines gC , hC , and i C , be drawn : then ( by cor . to theo . 13 ...
... measure BD : suppose that to be Ag , which will be contained twice in AB , and three times in BD , the parts Ag , gB , Bh , hi , and i D being all equal , and let the lines gC , hC , and i C , be drawn : then ( by cor . to theo . 13 ...
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acres altitude Answer arch base bearing blank line centre chains and links circle circle of latitude circumferentor Co-sec Co-tang column compasses contained decimal difference Dist divided divisions draw east Ecliptic edge EXAMPLE feet field-book figures fore four-pole chains geometrical series given angle given number half the sum Horizon glass hypothenuse inches instrument latitude length logarithm measure meridian distance minutes multiplied natural sine Nonius number of degrees object observed off-sets opposite parallelogram perches perpendicular plane pole pole star PROB proportion protractor Quadrant quotient radius right angles right line scale of equal SCHOLIUM screw Secant sect semicircle side sights square root station stationary distance subtracted survey taken tance Tang tangent theo theodolite trapezium triangle ABC trigonometry two-pole chains vane versed sine vulgar fraction whence
Δημοφιλή αποσπάσματα
Σελίδα 52 - 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 39 - The Circumference of every circle is supposed to be divided into 360 equal parts, called Degrees ; and each degree into 60 Minutes, each minute into 60 Seconds, and so on.
Σελίδα 18 - DISTINGUISH the given number into periods of two figures each, by putting a point over the place of units, another over the place of hundreds, and so on, which points shew the number of figures the root will consist of. 2. " FIND the greatest square number in the first, or left hand period...
Σελίδα 120 - 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.
Σελίδα 31 - 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 87 - On the line of lines make the lateral distance 10, a transverse distance between 8 on one leg, and 6 on the other leg. On the line of sines make the lateral distance 90, a transverse distance from 45 to 45 ; or from 40 to 50 ; or from 30 to 60 ; or from the sine of any degree to their complement.
Σελίδα 7 - RULE. Divide as in whole numbers, and from the right hand of the quotient point off as many places for decimals as the decimal places in the dividend exceed those in the divisor.
Σελίδα 82 - ... longer than the intermediate adjacent ones, these are whole degrees ; the shorter ones, or those of the third order, are 30 minutes. From the centre, to 60 degrees, the line of sines is divided like the line of tangents ; from 60 to 70, it is divided only to every degree ; from 70 to 80, to every two degrees ; from 80 to 90, the division must be estimated by the eye.