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" To trace Railroad Curves by means of deflections. General Propositions. 1. The angle formed by a tangent and a chord is equal to half the angle at the centre of the circle, subtended by the chord. 2. The angle of deflection formed by any two equal chords... "
A Collection of Tables and Formulę Useful in Surveying, Geodesy, and ... - Page 26
by Thomas Jefferson Lee - 1853 - 242 pages
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Mechanics Magazine, Volume 3

Industrial arts - 1825
...that is, the angle BAG is equal to half the number of degrees the arc AC measures, for the angle GDA is equal to half the angle at the centre of the circle (by Theorem n. Part п.), which is the measure of the arc AC. GAS (To be continued.} INQUIRIES. NO....
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Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - Electronic book - 1828 - 159 pages
...the figure itself will be a regular square inscribed in the circle. § 50. THEOREM. The angle made by a tangent and a chord is equal to half the angle at the centre subtended by that chord. Demonstr. From the centre C, draw the CD, perpendicular to the chord BA; this...
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Elements of the Geometry of Planes and Solids: With Four Plates

Ferdinand Rudolph Hassler - Electronic book - 1828 - 159 pages
...the figure itself will be a regular square inscribed in the circle. § 50. THEOREM. The angle made by a tangent and a chord is equal to half the angle at the centre subtended by that chord. APPLIC. In the circle BAE, (figure 56,) the chord BA, and the tangent FAG,...
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Mathematical Dictionary and Cyclopedia of Mathematical Science Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1859 - 592 pages
...method by Acjlcclions : This method depends upon the following elementary principles of Geometry : 1. The angle formed by a tangent and a chord is equal...the angle at the centre of the circle subtended by thc chord. 2. Thc angle of deflection formed by any cwo equal chords, meeting on the circumference,...
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The Mathematical Monthly, Volume 1

Mathematics - 1859
...straight lines, two and two. Since each of these lines is a common chord to two of the circles, and since the angle formed by a tangent and a chord is equal to the inscribed angle measured by the same arc, we have ABD = DAE and A CD = DAF. .-. ABD= the angle...
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Mathematical Dictionary and Cyclopedia of Mathematical Science: Comprising ...

Charles Davies, William Guy Peck - Mathematics - 1865 - 592 pages
...mclkod by deflections : This method depends upon the following elementary principles of Geometry : 1. The angle formed by a tangent and a chord is equal...deflection formed by any two equal chords, meeting on the circumference, is equal to the angle at the centre subtended by either chord. 3. A line bisecting...
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A Manual of Civil Engineering

William John Macquorn Rankine - Civil engineering - 1867 - 784 pages
...between the line drawn from one end of the arc and the prolongation of the line from the other end, that is equal to half the angle at the centre of the circle. When the point at which the angle is measured is one of the ends of the arc, as A, it is the angle...
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A Manual of Civil Engineering

William John Macquorn Rankine - Civil engineering - 1872 - 784 pages
...between the line drawn from one end of the arc and the prolongation of the line from the other end, that is equal to half the angle at the centre of the circle. When the point at which the angle is measured is one of the ends of the arc, as A, it is the angle...
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Professional Papers of the Corps of Engineers of the United States Army

United States. Army. Corps of Engineers - Military engineering - 1873
...5.63211 6.33613 Lat. 45° 8 9 U VI &J a o • л 1Л cu 3 i 6o 45 | 30 15 К 5' e ń СЛ • XIX.— To trace Railroad Curves by means of Deflections....tangent and a chord is equal to half the angle at the center of the circle subtended by the chord. 2. The angle of deflection formed by any two equal chords...
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A Manual of Civil Engineering

William John Macquorn Rankine - Civil engineering - 1883 - 808 pages
...between the line drawn from one end of the arc and the prolongation of the line from the other end, that is equal to half the angle at the centre of the circle. When the point at which the angle it measured is one of the ends of the arc, as A, it is the angle...
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