The Theory and Practice of Surveying: Containing All the Instructions Requisite for the Skilful Practice of this Art. With a New Set of Accurate Mathematical TablesHarper, 1832 - 348 páginas |
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Página 48
... measuring angles in general , has rendered the most important services to geography and navigation . THEOREM V. PL . 1. fig . 23 . In any triangle ABC , all the three angles , taken together , are equal to two right angles , viz . A + B ...
... measuring angles in general , has rendered the most important services to geography and navigation . THEOREM V. PL . 1. fig . 23 . In any triangle ABC , all the three angles , taken together , are equal to two right angles , viz . A + B ...
Página 49
... measured by half the arc it subtends or stands on . Fig . 26 . Cor . 2. Hence all angles at the circumference of a circle which ... measure of the angle ABC , C " must be greater than half a semicircle , that THEOREMS . 49 11 strated 191.
... measured by half the arc it subtends or stands on . Fig . 26 . Cor . 2. Hence all angles at the circumference of a circle which ... measure of the angle ABC , C " must be greater than half a semicircle , that THEOREMS . 49 11 strated 191.
Página 50
... measure them ( by def . 19 ) ; whence the arc AF = FB , and so AFB is bisected in F by the line CF. Cor . Hence the sine of an arc is half the chord of twice that arc . For AD is the sine of the arc AF ( by def . 20 ) , 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. Cor . Hence the sine of an arc is half the chord of twice that arc . For AD is the sine of the arc AF ( by def . 20 ) , AF is half the ...
Página 51
... measured by half the arc BKD ( by cor . 1 , theo . 7 ) , viz . the arc BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE , the half of BD , is the sine of BAD : in the same way may be proved that half of AD is ...
... measured by half the arc BKD ( by cor . 1 , theo . 7 ) , viz . the arc BK is the measure of the angle BAD ; therefore ( by cor . to the last ) BE , the half of BD , is the sine of BAD : in the same way may be proved that half of AD is ...
Página 53
... 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 ... measure of equal angles . THEOREM XVII . PL . 1. fig . 35 . THEOREMS . 53.
... 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 ... measure of equal angles . THEOREM XVII . PL . 1. fig . 35 . THEOREMS . 53.
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Términos y frases comunes
ABCD acres altitude arch azimuth base bearing blank line centre chains and links circle circumferentor co-sine column compasses contained cube root decimal diagonal diameter difference of latitude 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 logarithm manner measure meridian distance method multiplied needle nonius number of degrees object observed offsets opposite parallelogram perches perpendicular plane prob PROBLEM proportion protractor quadrant quotient radius rhombus right angles right line scale of equal SCHOLIUM screw secant sect sector semicircle side square root station stationary distance subtract suppose survey taken tangent theo theodolite THEOREM third trapezium triangle ABC trigonometry two-pole chains vane vulgar fraction whence
Pasajes populares
Página 173 - In like manner, when it is said, that " triangles on the same base, and between the same parallels, are equal...
Página 49 - 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 163 - RULE. From half the sum of the three sides subtract each side severally.
Página 41 - 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 97 - 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.
Página 41 - The radius of a circle is a right line drawn from the centre to the circumference.
Página 52 - Triangles upon equal bases, and between the same parallels, are equal to one another.
Página 24 - The square of the sum of two numbers is equal to the square of the first number plus twice the product of the first and second number plus the square of the second number.
Página 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.