I cannot do more than merely allude to the treatises on Conic Sections and on Maxima and Minima by Apollonius, who is said to have been the first to introduce the words ellipse and hyperbola.
Blaise Pascal, the French mathematician, composed at sixteen a tract on the conic sections.
The fact that the force varies as the inverse square of the distance, necessitates motion in an ellipse, or some other conic section, with the sun in one focus.
Hence three points plus the focus act as five points, and determine a conic or curve of the second degree.
If it were a material substance, to which the law of gravitation applied, it must be moving in a conic section with the sun in one focus, and its radius vector must sweep out equal areas in equal times.
To prove the connection between the inverse-square law of distance, and the travelling in a conic section with the centre of force in one focus (the other focus being empty), is not so simple.
He is famous for his theorem that a hexagon inscribed in a conic section has the property that the three meeting points of the opposed sides are always in a straight line.
It seemed a stupid way to commence his upper-class years, to spend four hours a morning in the stuffy room of a tutoring school, imbibing the infinite boredom of conic sections.
He found it impossible to study conic sections; something in their calm and tantalizing respectability breathing defiantly through Mr. Rooney's fetid parlors distorted their equations into insoluble anagrams.
If the Greeks had not cultivated Conic Sections, Kepler could not have superseded Ptolemy; if the Greeks had cultivated Dynamics, Kepler might have anticipated Newton.
There is a great deal of superstition about conic sections.
The discovery of the conic sections, attributed to Plato, first threw open the higher species of form to the contemplation of geometers.
A property of the conic sections by virtue of which a given point determines a corresponding right line and a given right line determines a corresponding point.
This projection differs from conic projection in that latter assumes but one cone for the whole map.
It consists of about thirty lodges or wigwams, formed generally of branches of trees tied together in a conic summit, and covered with buffalo, deer, or elk skins.
Our encampment this evening is on one of the head branches of the Blackfoot river, from which we can see the three remarkable conic summits known by the name of the "Three Butes" or "Tetons.
Or he may find a conic mound, on whose apex glisten in the sun the bleached bones of one whose last office has been to preserve from destruction the friendly soil on which he reposed.
We find the bubble curves can be drawn by rolling wheels made in the shape of the conic sections on a straight line, and so the conic sections, though distinct curves, must pass slowly and continuously one into the other.
It is the same shape that you would find if you were to cut a cone through with a saw, and so these curves which I have shown you are called conic sections.
We are now almost able to see what the conic section has to do with a soap-bubble.
The conic sections are the next simplest loci; and it will be seen later that they are the loci represented by equations of the second degree.
Every plane section of a quadric surface is a conicor a line-pair.
If the line does not cut the conic the involution is elliptic, having no foci.
The most important properties are stated in the following theorems:-- The middle points of parallel chords of a conic lie in a line--viz.
That it also holds for other conics follows from the fact that every conic may be considered as the projection of a circle, which will be proved later on.
If the line cuts the conic the involution is hyperbolic, the points of intersection being the foci.
If every diameter is perpendicular to its conjugate the conic is a circle.
Hence-- A conic determines on every line in its plane an involution, in which those points are conjugate which are also conjugate with regard to the conic.
Further-- Every parallelogram inscribed in a conic has its sides parallel to two conjugate diameters; and Every parallelogram circumscribed about a conic has as diagonals two conjugate diameters.
In excitement this prisoner had pushed the conic end up first, thus rendering expulsion almost impossible.
On investigation it was found that these conic cases were of common use, and were always thrust up the rectum base first.
I was beginning conic sections in the third half-year, and this subject I found was one that I could manage very well by thinking quietly over.
Apollonius investigated the greatest and least distances of a point from the perimeter of a conic section, and discovered them to be the normals, and that their feet were the intersections of the conic with a rectangular hyperbola.
Thus for a circular orbit with the centre of force at an excentric point, the hodograph is a conic with the pole as focus.
Round, a scale Of circling steps entwines the conic pile; And at the bottom on vast hinges grates Four brazen gates, towards the four winds of heaven Placed in the solid square.
Most likely it is the only copy of "O'Beirne on Conic Sections" existing in Ireland; and who would expect to find it lodged in a smoke-stained cabin on the wild bogland between Duffclane and Lisconnel?
The "Treatise on Conic Sections" created an even stronger sensation than the news of the honorary degree, especially among those who had letters enough to spell out the familiar name on the title-page.
I detest the very name of Parliament, and could as soon read Todhunter onConic Sections as the reports of a debate.
Waymark grew so accustomed to receiving Ida's note each Monday morning, that when for the first time it failed to conic he was troubled seriously.
The above list will hopefully give you a few useful examples demonstrating the appropriate usage of "conic" in a variety of sentences. We hope that you will now be able to make sentences using this word.
