The tangent PT at P is regarded as identical with the secant PQ, and the position of the tangent is determined by the similarity of the triangles PTM, PQR.
Then there is a point P between A and B at which the tangent is parallel to the secant AB.
If the curve has a tangent at P the secant PP' approaches a limiting position (see S 33 below).
For if from any point Q on the polar a secant be drawn cutting the conic in A and D (fig.
The two boundary non-secant lines, of which r and s are respectively halves, may be called the two parallels to l through A.
A secant improper may be considered, to use the language of coordinate geometry, as a secant with imaginary points of intersection.
Hence:-- Through every point in space not on the twisted cubic one and only one secant to the cubic can be drawn.
Every ray through S1 or S2 which is not a secant determines one of them.
C, D and the asymptotes in E, F, then the line OM which bisects the chord CD is a diameter conjugate to the diameter OK which is parallel to the secant t, so that OK and OM are harmonic with regard to the asymptotes.
It follows that DF = EC, and ED = CF; or On any secant of an hyperbola the segments between the curve and the asymptotes are equal.
I want secant fifteen less one times thirty-two hundred.
Projections for instance which are derived by geometrical construction from secant cones are very poor projections, exhibiting large errors, and they will not be discussed.
In some books this has been, most unfortunately, termed the "secant conical," on account of the fact that there are two parallels of the correct length.
There is no necessary connexion between a conical projection and any touching or secant cone.
The most useful conical projections have nothing to do with the secant cones, but are simply projections in which the meridians are straight lines which converge to a point which is the centre of the circular parallels.
The rectangle of the parts of a secant, comprised between a point of the curve and the asymptotes, is equal to the square of half of the diameter to which the secant is parallel.
The tangent is a mean proportional between thesecant and its exterior segment.
The locus of their centers is the diameter conjugate to that one of the secant planes which passes through the center of the surface.
The portions of a secantcomprised between the hyperbola and its asymptotes are equal.
Your correspondent ERYX inquires, in your paper of July 12, whether Servius's interpretation of "Viridesque secantplacido aequore silvas.
RPC be a portion of a curve such that at any point P the secant of the obliquity to the normal of the curve of a line parallel to the axis is inversely proportional to the ordinate PY, to which the velocity of P is proportional.
The following are the principles on which this equality of wear depends:-- The rapidity of wear of a surface measured in an oblique direction is to the rapidity of wear measured normally as the secant of the obliquity is to unity.
Defn: Cutting; divivding into two parts; as, a secant line.
Accordingly, an observation of the temperature produced by solar radiation at a zenith distance whose secant is twice that of the secant of 17° 12', viz.
And from these Measures I seem to gather this Rule: That the Thickness of the Air is proportional to the Secant of an Angle, whose Sine is a certain mean Proportional between the Sines of Incidence and Refraction.
If from a point without a circle a secant is drawn, the product of the secant and its external segment is constant in whatever direction the secant is drawn.
If from a point without a circle a secant and a tangent are drawn, the tangent is the mean proportional between the secant and its external segment.
An angle formed by two secants, a secant and a tangent, or two tangents, drawn to a circle from an external point, is measured by half the difference of the intercepted arcs.
