# Geometrically sentence example

geometrically
• Physical action is, therefore, impression, or transmission of force in lines, and must accordingly be explained geometrically.
• This may be readily accomplished geometrically or analytically, and it will be found that the envelope is a cardioid, i.e.
• It may be shown geometrically that the secondary Caustics caustic, if the second by refrac- medium be less refrac- tion.
• Such a curve may be regarded geometrically as actually described, or kinematically as in the course of description by the motion of a point; in the former point of view, it is the locus of all the points which satisfy a given condition; in the latter, it is the locus of a point moving subject to a given condition.
• But it can be shown, analytically or geometrically, that if the given curve has a node, the first polar passes through this node, which therefore counts as two intersections, and that if the curve has a cusp, the first polar passes through the cusp, touching the curve there, and hence the cusp counts as three intersections.
• Secondly, as to the inflections, the process is a similar one; it can be shown that the inflections are the intersections of the curve by a derivative curve called (after Ludwig Otto Hesse who first considered it) the Hessian, defined geometrically as the locus of a point such that its conic polar (§ 8 below) in regard to the curve breaks up into a pair of lines, and which has an equation H = o, where H is the determinant formed with the second differential coefficients of u in regard to the variables (x, y, z); H= o is thus a curve of the order 3 (m - 2), and the number of inflections is =3m(m-2).
• The power and spirit of the analytic method will be appreciated by showing how it expresses the relations of motion as they were conceived geometrically by Newton and Kepler.
• Having these data, the position of the planet at any other time may be geometrically constructed by Kepler's laws.
• Alain even ventures an immediate application of this principle, and tries to prove geometrically the dogmas defined in the Creed.
• The Aziz version is a post-modern deconstructed geometrically arranged stuffed eggplant dish made with halved baby eggplants.
• It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the isothermal compressibility by means of the geometrically obvious relation, BE = (BEÃƒâ€ C) XEC. The ratio BEÃƒâ€ C of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.
• It was especially used to represent geometrically the periodic apparent retrograde motion of the outer planets, Mars, Jupiter and Saturn, which we now know to be due to the annual revolution of the earth around the sun, but which in the Ptolemaic astronomy were taken to be real.
• Finials are geometrically shaped or the rods have end caps.
• There is no linear covariant, since it is impossible to form a symbolic product which will contain x once and at the same time appertain to a quadratic. (v.) is the Jacobian; geometrically it denotes the bisectors of the angles between the lines ax, or, as we may say, the common harmonic conjugates of the lines and the lines x x .
• He solved quadratic equations both geometrically and algebraically, and also equations of the form x 2 "+ax n +b=o; he also proved certain relations between the sum of the first n natural numbers, and the sums of their squares and cubes.
• Cubic equations were solved geometrically by determining the intersections of conic sections.
• The method of solving equations geometrically was considerably developed by Omar Khayyam of Khorassan, who flourished in the 1 r th century.
• By applying the method of the differential calculus, we obtain cos i= { (µ 2 - 1)/(n24-2n)} as the required value; it may be readily shown either geometrically or analytically that this is a minimum.
• It is often impossible to observe the pressure-coefficient dp/de directly, but it may be deduced from the isothermal compressibility by means of the geometrically obvious relation, BE = (BEÃ†C) XEC. The ratio BEÃ†C of the diminution of pressure to the increase of volume at constant temperature, or - dp/dv, is readily observed.
• This is geometrically obvious from the form of the area representing the function on the indicator diagram, and also follows directly from the first law.
• His method of estimating the relative lunar and solar distances is geometrically correct, though the instrumental means at his command rendered his data erroneous.
• The circle, for instance, is regarded geometrically as a line described in a particular way, while from the point of view of mensuration it is a figure of a particular shape.
• Although Hippocrates could not determine the proportionals, his statement of the problem in this form was a great advance, for it was perceived that the problem of trisecting an angle was reducible to a similar form which, in the language of algebraic geometry, is to solve geometrically a cubic equation.
• Beside the equivalence of the hon to 5 utens weight of water, the mathematical papyrus (35) gives 5 besha = (2/3)cubic cubit (Revillout's interpretation of this as 1 cubit cubed is impossible geometrically; see Rev. Eg., 1881, for data); this is very concordant, but it is very unlikely for 3 to be introduced in an Egyptian derivation, and probably therefore only a working equivalent.
• Pappus gives several solutions of this problem, including a method of making successive approximations to the solution, the significance of which he apparently failed to appreciate; he adds his own solution of the more general problem of finding geometrically the side of a cube whose content is in any given ratio to that of a given one.