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 47
... angle ACE = A ( by part 2 of the last ) , therefore ECD + ACE = ACD = B + A . Q. E. D. Cor . 1. Hence , if a triangle have its exterior angle and one of its opposite interior angles double of those in another tri- angle , its remaining ...
... angle ACE = A ( by part 2 of the last ) , therefore ECD + ACE = ACD = B + A . Q. E. D. Cor . 1. Hence , if a triangle have its exterior angle and one of its opposite interior angles double of those in another tri- angle , its remaining ...
Página 48
... angles ( by theo . 1 ) ; there- fore the three angles A + B + ACB = two right angles . Q. E. D. Cor . 1. Hence if one angle of a triangle be known , the sum of the other two is also known ; for since the three angles of every triangle ...
... angles ( by theo . 1 ) ; there- fore the three angles A + B + ACB = two right angles . Q. E. D. Cor . 1. Hence if one angle of a triangle be known , the sum of the other two is also known ; for since the three angles of every triangle ...
Página 49
... angle BCD at the centre of a circle ABED is double the angle BAD at the circumference , standing upon the same arc BED . Through the point A , and the centre C , draw the line ACE ; then the angle ECD = CAD + CDA ( by theo . 4 ) ; but ...
... angle BCD at the centre of a circle ABED is double the angle BAD at the circumference , standing upon the same arc BED . Through the point A , and the centre C , draw the line ACE ; then the angle ECD = CAD + CDA ( by theo . 4 ) ; but ...
Página 50
... angle in a semicircle is a right angle , for the mea- sure of the angle ABD is half of a semicircle AED , and therefore a right angle . THEOREM VIII . PL . 1. fig . 29 . If from the centre C of a circle ABE there be let fall the ...
... angle in a semicircle is a right angle , for the mea- sure of the angle ABD is half of a semicircle AED , and therefore a right angle . THEOREM VIII . PL . 1. fig . 29 . If from the centre C of a circle ABE there be let fall the ...
Página 51
... angle . Let the circle ADB be drawn through the points A , B , D ; then the angle DAB 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 ...
... angle . Let the circle ADB be drawn through the points A , B , D ; then the angle DAB 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 ...
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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.