The Theory of Deflections and of Latitudes and Departures: With Special Application to Curvilinear Surveys for Alignments of Railway-tracksD. Van Nostrand, 1884 - 229 páginas |
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The Theory of Deflections and of Latitudes and Departures: With Special ... Isaac W. Smith Sin vista previa disponible - 2017 |
The Theory of Deflections and of Latitudes and Departures: With Special ... Isaac W. Smith Sin vista previa disponible - 2017 |
Términos y frases comunes
½ F ½ Ia ½ Ib ½ Xa 180 degrees 90 degrees A'+B AB.CD abscissa acute angles algebraic difference algebraic sum alignment of curves axis calculated bearing centres chord deflection circle ATB co-ordinates common tangent compound curves compound or reversed concave convex crossing curve ordinates decimals degree of curvature departure and latitude determined different sides double switches equation Example 1 figure feet following formula frog frog-angle frog-circle frog-distances given greater i÷sin Ia and Ib Ia+Ib initial point initial tangent inside length magnetic bearing main-track rail measured middle ordinate minus minus the bear negative number of stations opposite perpendicular positive Prob problem XVIII quantities radii radius railroad-track reversed curves right angles right or left rules of problem sign and magnitude sign prefixed straight line subtracting switch-angle tangent arc tangent-point tangential deflection tangential ordinate TaTb terminal tangent three-throw switches tion turn-out curve vers versin
Pasajes populares
Página 69 - Thus, that the square of the hypothenuse of a right-angled triangle is equal to the sum of the squares of the other two sides, was an experimental discovery, or why did the discoverer sacrifice a hecatomb when he made out its proof ?
Página 67 - Greek philosopher, and mathematician that the area of the square described on the hypotenuse of a rightangled triangle is equal to the sum of the areas of the squares described on the other two sides.
Página 11 - The COSINE of an arc, is the sine of the complement of •that arc, and is equal to the part of the radius comprised between the centre of the circle and the foot of the sine.
Página 11 - The sine of an arc is the perpendicular let fall from one extremity of the arc on the diameter which passes through the other extremity.
Página 67 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Página 11 - BAC, or CAB, the letter at the vertex being always placed in the middle. Angles, like all other quantities, are susceptible of addition, subtraction, multiplication, and division. Thus the angle DCE is the sum of the two angles DCB, BCE ; and the angle DCB is the difference of the two angles DCE, BCE.
Página 11 - ... point, after commencing its motion, does not change its direction, the path described will be a straight line. From this, distance and limitation are excluded, and the mind has to consider the direction alone. Moreover by adopting this definition, we avoid the necessity of demonstrating theorem 32 ; ' Two straight lines, which have two points common, coincide throughout, and form one and the same straight line.
Página 33 - ... taken as the correct result. The distance must then be measured, which will furnish all the data required to find the difference of level between the places of the instrument and staff; this, it will appear evident, is a matter of trigonometrical calculation,* the measured distance being considered as the hypothenuse of a right-angled triangle, of which the perpendicular is the difference of level. It scarcely appears necessary to give the rule for the calculation, but for the sake of uniformity...
Página 73 - ... same reason, the angle C is equal to the angle EBC. Hence, the three angles of the triangle are equal to the three consecutive angles at the point B, which are equal to two right angles (91). Therefore, the sum of the three angles of the triangle is equal to two right angles. 256. Corollary — Each angle of a triangle is the supplement of the sum of the other two.
Página 65 - DE, with the usual conventions as to directed line segments, positive when measured to the right and negative when measured to the left...