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 46
... circumference : thus LB is the versed sine of the arc HB . fig . 8 . 22. The tangent of an arc is a right line touch- ing the periphery , being perpendicular to the end of the diameter , and is terminated by a line 46 GEOMETRY .
... circumference : thus LB is the versed sine of the arc HB . fig . 8 . 22. The tangent of an arc is a right line touch- ing the periphery , being perpendicular to the end of the diameter , and is terminated by a line 46 GEOMETRY .
Σελίδα 49
... perpendicular height of a triangle is a line drawn from the vertex to the base perpen- dicularly thus if the triangle ABC , be propos- ed , and BC be made its base , then if from the vertex A the perpendicular AD be drawn to BC , the ...
... perpendicular height of a triangle is a line drawn from the vertex to the base perpen- dicularly thus if the triangle ABC , be propos- ed , and BC be made its base , then if from the vertex A the perpendicular AD be drawn to BC , the ...
Σελίδα 52
... perpendicular to CD , then ( by def . 10. ) the angles CBA , and ABD , will be each a right angle . 2. But if the line fall slantwise , as EB , and let AB be perpendicular to CD ; then the 2 DBA = DBE + EBA , add ABC to each ; then ...
... perpendicular to CD , then ( by def . 10. ) the angles CBA , and ABD , will be each a right angle . 2. But if the line fall slantwise , as EB , and let AB be perpendicular to CD ; then the 2 DBA = DBE + EBA , add ABC to each ; then ...
Σελίδα 58
... right angled ones , since the line CD is a perpendicular ; and so the angle ACD = DCB ; ( by cor . 2. theo . 5. ) then have we AC , CD , and the angle ACD in one tri- angle ; severally equal to CB , CD , and 58 GEOMETRICAL.
... right angled ones , since the line CD is a perpendicular ; and so the angle ACD = DCB ; ( by cor . 2. theo . 5. ) then have we AC , CD , and the angle ACD in one tri- angle ; severally equal to CB , CD , and 58 GEOMETRICAL.
Σελίδα 59
... perpendicular to a chord , bisects that chord at right angles ; there- fore , conversely , a line bisecting a chord at right angles must pass through the centre , and conse- quently be a diameter . THEO . IX . PL . 1. fig . 29 . If from ...
... perpendicular to a chord , bisects that chord at right angles ; there- fore , conversely , a line bisecting a chord at right angles must pass through the centre , and conse- quently be a diameter . THEO . IX . PL . 1. fig . 29 . If from ...
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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.