# secant

## Definitions

• WordNet 3.6
• n secant ratio of the hypotenuse to the adjacent side of a right-angled triangle
• n secant a straight line that intersects a curve at two or more points
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Webster's Revised Unabridged Dictionary
• Secant (Geom) A line that cuts another; especially, a straight line cutting a curve in two or more points.
• Secant (Trig) A right line drawn from the center of a circle through one end of a circular arc, and terminated by a tangent drawn from the other end; the number expressing the ratio of this line to the radius of the circle. See Trigonometrical function, under Function.
• a Secant sē"kănt Cutting; dividing into two parts; as, a secant line.
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Century Dictionary and Cyclopedia
• secant Cutting; dividing into two parts.
• n secant A line which cuts a figure in any way.
• n secant Specifically, in trigonometry, a line from the center of a circle through one extremity of an are (whose secant it is said to be) to the tangent from the other extremity of the same are; or the ratio of this line to the radius; the reciprocal of the cosine.
• secant Specifically, noting a stream which cuts across folded strata.
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Chambers's Twentieth Century Dictionary
• adj Secant sē′kant cutting: dividing
• n Secant a line that cuts another: a straight line from the centre of a circle to one extremity of an arc, produced till it meets the tangent to the other extremity
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## Etymology

Webster's Revised Unabridged Dictionary
L. secans, -antis, p. pr. of secare, to cut. See Section

## Usage

### In literature:

The whole secret of avoiding shipwreck is to try and pass from the secant to the tangent.
"The Man Who Laughs" by Victor Hugo
He felt the necessity of gaining a more firm footing, and turned toward the road by the shortest secant line.
"The Vicomte de Bragelonne" by Alexandre Dumas
I want secant fifteen less one times thirty-two hundred.
"Skylark Three" by Edward Elmer Smith
The complement of the logarithm of a sine, tangent, or secant.
"The Sailor's Word-Book" by William Henry Smyth
Add together the secant of the Latitude, the cosecant of the P.D., the cosine of the Half Sum and the sine of the Difference (Table 44).
"Lectures in Navigation" by Ernest Gallaudet Draper
DEF, is termed a "secant"; if it touches the circle, e.g.
"Encyclopaedia Britannica, 11th Edition, Volume 6, Slice 4" by Various
His father stood over him in wonder while he filled a sheet of paper with sines, cosines, secants, and such things.
"Harper's Round Table, June 4, 1895" by Various
The lines where a plane cuts its corresponding plane are secants.
"Encyclopaedia Britannica, 11th Edition, Volume 11, Slice 6" by Various
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### In news:

Secant Medical to Highlight the Device Design Benefits of Implantable Textiles at BIOMEDevice San Jose.
Barbara Rice, a yarn prep technician, operates a Creel machine at Secant Medical's plant in Quakertown during a visit last year by Gov Tom Corbett.
Secant Medical Receives Frost & Sullivan 2012 Enabling Technology Award Industry Analyst Distinguishes Medical Implantable Textile Structures Design Approach.
Secant Medical Appoints Peter Gabriele as Director, Emerging Technology.
Yarn prep manager Alan Kiefer (right) explains how the ring twister machine operates to Pennsylvania Governor Tom Corbett during his tour of Secant Medical on Monday in Quakertown, Pa. Buy Intelligencer photos.
Barbara Rice, a yarn prep technician, operates a Creel machine at Secant Medical's new plant in Quakertown, Pa. Pennsylvania Governor Tom Corbett toured the facility Monday.
Secant Medical senior engineer Ryan Heniford (left) explains a piece of surgical mesh to Pennsylvania Governor Tom Corbett at the company's new facilities in Quakertown, Pa. Buy Intelligencer photos.
In developing DISCUS' data collection system, Elena Amboyan and Anne Carlson, Secant 's managing partners, worked closely with DISCUS members and conducted interviews to review their historic data research needs.
DISCUS Selects Secant For Sales Data.
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### In science:

For ∂ general, there are exactly six distinct secants to C that contain [∂ ], none of which is trisecant or tangent.
Ampleness of intersections of translates of theta divisors in an abelian fourfold
Since the set of secants to C is irreducible, if one of these translates is contained in Θ ∩ ∂Θ ∩ ∂ 2Θ for ∂ general, they all are.
Ampleness of intersections of translates of theta divisors in an abelian fourfold
For the envelope ¯EX (t) we have chosen the hyperbolic secant shape.
Attosecond streaking experiments on atoms: quantum theory versus simple model
The number of points in the intersection of two secant lines with a conic (non-singular plane quadric) is exactly four or less than three.
Codes defined by forms of degree 2 on quadric and non-degenerate hermitian varieties in \$\mathbb{P}^{4}(\mathbb{F}_q)\$}
Indeed, if ˆXi ∩ ˆQi contains more than one line, from the fact that one of the two quadrics ˆXi or ˆQi is a quadric cone, they are secant.
Codes defined by forms of degree 2 on quadric and non-degenerate hermitian varieties in \$\mathbb{P}^{4}(\mathbb{F}_q)\$}
For type 3, if ˆXi ∩ ˆQi contains exactly four common lines, then it contains necessarily two secant lines.
Codes defined by forms of degree 2 on quadric and non-degenerate hermitian varieties in \$\mathbb{P}^{4}(\mathbb{F}_q)\$}
D1 , D2 } denote a pair of secant lines and P be the plane generated by this pair of secants.
Codes defined by forms of degree 2 on quadric and non-degenerate hermitian varieties in \$\mathbb{P}^{4}(\mathbb{F}_q)\$}
If Q ∩ X contains at least two common lines: We distinguish two cases: Q ∩ X containing only skew lines or some secant lines.
Codes defined by forms of degree 2 on quadric and non-degenerate hermitian varieties in \$\mathbb{P}^{4}(\mathbb{F}_q)\$}
Otherwise ˆQi would contain two secant lines of ˆXi .
Codes defined by forms of degree 2 on quadric and non-degenerate hermitian varieties in \$\mathbb{P}^{4}(\mathbb{F}_q)\$}
If Q ∩ X contains some secant lines, let (D1 ) and (D2 ) be two of them (which are not skew) and P the plane generated by them.
Codes defined by forms of degree 2 on quadric and non-degenerate hermitian varieties in \$\mathbb{P}^{4}(\mathbb{F}_q)\$}
Draisma, A tropical approach to secant dimensions. J.
Generic Tropical Varieties
As the acceleration increases, all harmonics broaden, developing exponential tails in the power spectrum which can be approximated by the squared hyperbolic secant function sech2 [b(f − fn )].
Phase randomization of three-wave interactions in capillary waves
The shape of these modulation envelopes is well approximated by a hyperbolic secant, s(t) = sech(π2/b t).
Phase randomization of three-wave interactions in capillary waves
Draisma, A tropical approach to secant dimensions. J.
Algebraic Properties of Generic Tropical Varieties
Let ℓ be the line of direction v , and for any x ∈ H , denote by σ(x) the secant K ∩ (x + ℓ), and by M (x) the midpoint of σ(x).
Stability results for the volume of random simplices
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