## An Essay on the Theory and Practice of Setting Out Railway Curves |

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actual sine adjusted angle of deflection angle ẞ angles measured angular quantity apex ascertain calculate centre chains chord circle clear curve determine diagram direction distance divide drive effected equal equi-distant error Euclid Euclid 32 explained extend fixed formed formula four give given ground half half the angle hand internal angle joining junction laid latter length line of collimation lines and angles logarithm mathematical means minute move Natural Sines necessary Observations offsets opposite angles plug point of intersection practice precision principles proceed proportional quantity ẞ radiating Railway rationale relations respectively right angles side sight sine angle sine of 90 sine of half straight line straight portions subchord successive supplement supposing tables tabular radius tabular sine tangent tangent points termination thence Theodolite triangle whole arc

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Page 23 - ... double of that which measures the opposite angle ; that is, double the sine of that angle measured in the circle ; therefore the sides of the triangle are to each other as the sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in the circle whose radius is that of the tables.

Page 23 - ... as the sines of the opposite angles measured in the same circle, and consequently as the sines of the same angles measured in the circle whose radius is that of the tables. Hence the following proposition...