A clear conception of this fact led almost immediately to the Method of Tangents of Fermat and Barrow; and this again is the stepping-stone to the Differential Calculus,--itself a particular application of that instrument.
She went off at one of her inevitable tangents so useful in order to dodge issues.
Logarithms of the ratios of arcs to tangents from 0^q.
In the same year Vlacq published at Gouda his Trigonometria artificialis, giving log sines and tangents to every 10 seconds of the quadrant to 10 places.
The title of Gunter's book, which is very scarce, is Canon triangulorum, and it contains logarithmic sines and tangentsfor every minute of the quadrant to 7 places of decimals.
Any two tangents to a parabola are cut by all others in projective rows; but the line at infinity being one of the tangents, the points at infinity on the rows are corresponding points, and the rows therefore similar.
The tangentsat the two points at infinity are finite because the line at infinity is not a tangent.
If we now draw a second line through P, cutting the conic in C and D, then the point M harmonic conjugate to P with regard to CD, and the point G where the tangents at C and D meet, must also lie on p.
It has the property that on the side p opposite P meet the tangents at A and B, and also those at C and D.
The tangents at a point of a surface which bisect the angles between the chieftangents are called the principal tangents at the point.
The statement of the proposition and its whole treatment show the difficulties which the tangents presented to Euclid.
At a special point which is such that the chief tangents there run to the circular points at infinity in the tangent plane, the principaltangents are indeterminate; such a special point is called an umbilic of the surface.
On the other hand the curve of the second class is more than determined by the three tangents a, b, c and their points of contact A, B, C, so that d is any tangent to this curve.
A surface of any order is covered by two singly infinite systems of curves, a pair through every point, thetangents to which are all chief tangents at their respective points of contact.
Hence also-- From the centre of an hyperbola two tangents can be drawn to the curve which have their point of contact at infinity.
Given five points on a curve of Given five tangents to a curve second order to construct the of second class to construct the tangent at any one of them.
This same store included in its stock such heterogeneous objects, so utterly irrelevant to one another and at such tangents of connection, that it seemed sometimes like a very mad-house of trade.
All the free lines in the room were the tangents of irrelevancy and disorder.
The problem of maxima and minima and the problem of tangents had also by the same time been effectively solved.
If u1 also vanishes, the origin is a double point and u2 = o represents the tangents at the origin.
Whatever indistinctness might be felt to attach to the symbols, the processes for solving problems of tangents and of maxima and minima were reduced once for all to a definite routine.
Newton added applications of his methods to maxima and minima, tangents and curvature.
Roberval and Torricelli could construct the tangents of many curves, but they did not arrive at Fermat's artifice.
In this problem oftangents also Fermat found the required result by a process equivalent to differentiation.
Other methods for the solution of the problem of tangents were devised by Roberval and Torricelli, and published almost simultaneously in 1644.
In connexion with the problem oftangents the differentials are said to be proportional to the momentary increments of the abscissa and ordinate.
Only on question of the hearing of sound-signals in fog do we throw our weight about, and we make reminiscent tangents not wholly connected with the point at issue.
His own brain shot off at queer tangents and led him constantly into unexpected places.
It whirled and shot off at unexpected tangents and danced as irresponsibly as a grasshopper from one place to another.
We may from each of the circular points draw tangents to a given curve; the intersection of two such tangents (belonging of course to the two circular points respectively) is a focus.
A non-singular quartic has only even circuits; it has at most four circuits external to each other, or two circuits one internal to the other, and in this last case the internal circuit has no double tangents or inflections.
In addition to these lines he proceeds to mention the circle giving the ordinary division into degrees and minutes, and two circles of tangents on the other side of the rule.
Let the paralleltangents meet one of the other tangents in A and B and the other in C and D, and let P and Q be the points of contact of the parallel tangents R and S of the others.
Furthermore, since the tangents at L and N meet on this same line, it appears as the locus of intersections of pairs of tangents drawn at the extremities of chords through O.
To construct the conic" means here to draw as many other tangents as may be desired.
Thus the tangents to a circle are seen to join corresponding points on two projective point-rows, and so, according to the definition, form a pencil of rays of the second order.
Apply the theorem of problem 9 to the case of a hyperbola where the two tangents are the asymptotes.
Brianchon’s theorem may also be used to solve the following problems: Given four tangents and the point of contact on any one of them, to construct other tangents to a conic.
To get a clear notion of this system of lines, we may first show that the tangents to a circle form a system of this kind.
As previously noted, these two tangents are called the asymptotes of the curve.
The double rays, if any exist, are thetangents from the point to the conic.
The tangentsto a curve at its infinitely distant points are called its asymptotes if they pass through a finite part of the plane.
If a conic of the system should go through the fixed point, it is clear that the two tangents would coincide and indicate a double ray of the involution.
It is possible, therefore, to make the following definition: Four tangents to a conic are said to be harmonic when they meet every other tangent in four harmonic points.
Accordingly, I shall neither waste time in dwelling on the guilt of this man before you, from whose cruelty you have rescued yourselves by force of arms, nor will I suffer him to add impudence to his other crimes in defending himself.
Immediately after Duillius carried a proposition for electing consuls, with right of appeal[59].
When he entered on his tribuneship, Lucius Icilius immediately brought before the people, and the people enacted, that the secession from the decemvirs which had taken place should not prove detrimental to any individual.
Hence thetangents at A and B to the upper catenary must intersect above the directrix, and the tangents at A and B to the lower catenary must intersect below the directrix.
This catenoid, however, is in stable equilibrium only when the portion considered is such that the tangentsto the catenary at its extremities intersect before they reach the directrix.
The condition of stability of a catenoid is therefore that the tangents at the extremities of its generating catenary must intersect before they reach the directrix.
A tangent plane to the surface at t cuts the plane of projection in the line rvs perpendicular to ov; tv is a tangent to the circle kt at t, tr and ts are any two tangents to the surface at t.
Join CQ, C'Q'; these being perpendicular to the circles will betangents to the curve.
In both, the strings are struck--by metal tangents in the clavichord and by leather or felt hammers in the piano.
Tangents on keys numbered 16 and 17 strike the same strings to produce the notes e-flat and e.
Produce these tangents till they meet at point S, which will be the point of sight.
From A and B draw two other tangents so that they shall touch the curve at points such as TT· a little above the transverse diameter and on a level with each other.
To construct the intersection of two oblique cones, and the tangents to that curve.
Construction of tangent planes to surfaces, of curves, of intersection of surfaces, of their tangentsand their assymplotes.
Tangents and normals to plane curves, whose equation in linear or polar coordinates is given.
To find the tangent of the sum or of the difference of two arcs, knowing the tangents of those arcs.
The two lines of curvature which cross at a point, aretangents to the principal sections of the surface at that point.
The determination of tangents will be effected in the most general manner by means of the derivatives of the various functions, which we inserted in the programme of algebra.
Construction of the tangents to this curve of intersection.
To construct the intersection of a surface of revolution by a plane, and the tangents to the curve of intersection.
To construct the intersection of two cylindrical surfaces, and the tangents to that curve.
Since those Tangents continue to be right Lines, every Circle which in the first Prism is more or less refracted, is exactly in the same proportion more or less refracted in the second.
Since the distance between those Tangents or breadth of the Spectrum is not increased by the Refractions, the Diameters of the Circles are not increased thereby.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "tangents" in a variety of sentences. We hope that you will now be able to make sentences using this word.
