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" The tangent of an arc is a right line touching the circumference, and drawn perpendicular to the diameter ; and is terminated by a line drawn from the centre through the other end of the arc ; thus BK is the tangent of the arc BH. "
A System of Geometry and Trigonometry: With a Treatise on Surveying ... in ... - Page 13
by Abel Flint - 1830 - 284 pages
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Elements of Geometry and Trigonometry from the Works of A. M. Legendre ...

Adrien Marie Legendre, Charles Davies - Geometry - 1857 - 432 pages
...have occasion to refer to but one circular function not already defined. It is called the versed sine. The versed sine of an arc, is that part of the diameter intercepted between the point where the measuring arcs begin and the foot of the sine. It is designated,...
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ELEMENTS OF PLANE AND SPHERICAL TRIGONOMETRY

ELIAS LOOMIS, LL.D. - 1859
...the radius (Geom., Prop. IV., B. VI.) ; hence the sine of 30 is equal to half of the radius. (23.) The versed sine of an arc is that part of the diameter intercepted between the sine and the arc. Thus GrA is the versed sine of the arc AF. (24). The tangent...
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A Treatise on Practical Mensuration

Anthony Nesbit - Measurement - 1859 - 450 pages
...arc ; DG is also the tangent of the arc AE, and CG the secant of the arc AE, the supplement of AD. The versed sine of an arc is that part of the diameter contained between the sine and the arc ; thus FD is the versed sine of the arc AD, and FE is the versed...
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A practical treatise on ... land and engineering surveying, Volume 34

Henry S. Merrett - 1863
...the arc perpendicular to the diameter, as BF, or the supplement to the arc BD E. (Fig. 1, Plate 28.) The versed sine of an arc is that part of the diameter intercepted between the arc and its sine ; as AF is the versed sine of the arc A B. The tangent of...
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A Practical Treatise on the Science of Land and Engineering Surveying ...

Henry S. Merrett - Surveying - 1863 - 317 pages
...degrees. The sine of an arc is a line drawn from one extremity of an arc, perpendicular to the diameter. The versed sine of an arc is that part of the diameter intercepted between the arc and its sine. The tangent of an arc is a line drawn perpendicular to the...
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The Quadrature of the Circle: The Square Root of Two, and the Right-angled ...

William Alexander Myers - Circle-squaring - 1873 - 164 pages
...radius (Loomis, Gcom., Prop. IV., Book VI.); hence the sine of 30 is equal to half of the radius. The versed sine of an arc is that part of the diameter intercepted between the sine and the arc. Thus GA is the versed sine of the arc AF, The tangent of...
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THE QUADRATURE OF THE CIRCLE, THE SQUARE ROOT OF TWO, AND THE RIGHT-ANGLED ...

WILLIAM ALEXANDER MYERS - 1874
...radius (Loomis* Geom., Prop. IV., Book VI.); hence the sine of 30 is equal to half of the radius. The, versed sine of an arc is that part of the diameter intercepted between the sine and the arc. Thus GA is the versed sine of the arc AF. The tangent of...
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - Geometry - 1877 - 443 pages
...tangent, and secant of one of these angles is the cosine, cotangent, and cosecant of the other. 12. The versed sine of an arc is that part of the diameter intercepted between the extremity of the arc and the foot of the sine. Thus GA is the versed sine of...
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The American Practical Navigator: Being an Epitome of Navigation and ...

Nathaniel Bowditch - Nautical astronomy - 1888 - 647 pages
...SI I is the complement of the arc AS; S/. is the sine of the arc Sil, or the cosine of the arc AS. The versed sine of an arc is that part of the diameter contained between the sine and the arc ; thus, RA is the versed sine of the arc AS, and DCR is the...
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The Mechanical Engineer's Pocket-book: A Reference Book of Rules, Tables ...

William Kent - Engineering - 1902 - 1113 pages
...arc is that part of the proditced diameter which is intercepted betn-een the centre and the tangent. The versed sine of an arc is that part of the diameter intercepted beticeen the extremity of the arc and the foot of the sine. In a circle whose radius is...
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