Chapter 10 : Quadratic Relations and Conic Sections
History of Conic Sections

History of Conic Sections
Apollonius of Perga (about 262-200 B.C.) was the last of the great mathematicians of the golden age of Greek mathematics. Apollonius, known as "the great geometer," arrived at the properties of the conic sections purely by geometry. His descriptions were so complete that he would have had little to learn about conic sections from our modern analytical geometry except for the improved modern notation. He did not, however, describe the properties of conic sections algebraically as we do today. It would take almost 2000 years before mathematicians would make great advances in the understanding of conic sections by combining both geometric and algebraic techniques. Apollonius defined the conic sections as sections of a cone standing on a circular base. The cone did not have to be a right cone, but could be slanted, or oblique. Apollonius noticed that all sections cut through such a cone parallel to its base were circles. He then extended the properties that he observed from these circles to ellipses and the other conic sections. He even solved the difficult problem of finding the shortest and longest distances from a given point to a conic section. These distances lie on lines called normals, which cut the curve of a conic section at right angles. Trying to read Apollonius' work, however, is not easy even with the best modern translation. Not only was his work very general in that it could be applied to many different situations involving conic sections, but it was also very long and rigorous, following the exacting principles of Euclidean proof. This is why the works of mathematicians like Hypatia, written several centuries later, were so important. Readers of Apollonius' Conics are better able to understand this text with the aid of these other texts that make the principles easier to understand. It is fortunate that scientists like Johannes Kepler, who...

...AN INTRODUCTION TO CONICSECTIONS
There exists a certain group of curves called ConicSections that are conceptually kin in several astonishing ways. Each member of this group has a certain shape, and can be classified appropriately: as either a circle, an ellipse, a parabola, or a hyperbola. The term "ConicSection" can be applied to any one of these curves, and the study of one curve is not essential to...

...
1.
(a) Indications
-The stenopaic slit refraction is useful for confirming the results of other refraction techniques for patients with irregular astigmatism or reduced visual acuity.
- It is helpful for patients who have difficulty understanding the complex instructions associated with other subjective techniques.
-It is important to note that, like the pinhole, the stenopaic slit may be used diagnostically to determine a patient's potential visual acuity.
-The astigmatism present in the...

...Chapter 13_Graphing the ConicSections
Ellipses
In this study guide we will focus on graphing ellipses but be sure to read and understand
the definition in your text.
Equation of an Ellipse (standard form)
Area of an Ellipse
( x − h) 2 ( y − k ) 2
+
=1
a2
b2
with a horizontal axis that measures 2a units, vertical axis
measures 2b units, and (h, k) is the center.
The long axis of an ellipse is called the major axis and the short
axis is...

...epigraphy, numismatics, monuments Literary sources: Indigenous: Primary and secondary; poetry, scientific literature, literature, literature in regional languages, religious literature. Foreign accounts: Greek, Chinese and Arab writers.
2. Pre-history and Proto-history: Geographical factors; hunting and gathering (paleolithic and mesolithic); Beginning of agriculture (neolithic and chalcolithic).
3. Indus Valley Civilization: Origin, date, extent,...

...what retinal tears and detachments are. It discusses
their symptoms, causes, diagnosis and
Lens
treatment options.
Cornea
Anatomy
It is important to recognize the parts of the
eye before learning about retinal tears and
detachments. This section reviews the
anatomy of the eye.
Light hits the cornea of the eye first. The
cornea is the transparent covering on the
front of the eye.
Iris
Vitreous
Macula
Retina
Next, light travels to the back part of the...

...A conic or conicsection is a plane curve that can be obtained by intersecting a cone with a plane that does not go through the vertex of the cone. There are three possibilities, depending on the relative position of the cone and the plane. If no line of the cone is parallel to the plane, the intersection is a closed curve, called an ellipse. If one line of the cone is parallel to the plane, the intersection is an open curve whose two ends are...

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...
Today one of the most cherished ideologies of America is the fact that everyone is and should be created equal. With this cherished ideology bringing a sense of pride and diversity to America we must keep in mind that this cherished ideology did not always exist. Since 1865 various individuals and groups have not been able to receive and express their rights to full equal status in the United States. These different individuals and groups have seemingly fought for their rights in...

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