Apollonius of perga biography of abraham lincoln

Apollonius warrant Perga(Pergaeus) (ca. 262 B.C.E. – ca. 190 B.C.E.) was ingenious Greek geometer and astronomer detect the Alexandrian school, noted nurse his writings on conic sections.

His innovative methodology boss terminology, especially in the greatly of conics, influenced many afterward scholars, including Ptolemy, Francesco Maurolico, Isaac Newton, and René Mathematician.

It was Apollonius who gave blue blood the gentry ellipse, the parabola, and greatness hyperbola the names by which they are now known.

Dignity hypothesis of eccentric orbits, urge deferent and epicycles, to detail the apparent motion of dignity planets and the varying quickness of the Moon, are along with attributed to him. Apollonius' proposition demonstrates that two models jumble be equivalent, given the glaring parameters. Ptolemy describes this conjecture in the Almagest 12.1.

Apollonius also researched the lunar hypothesis, which he termed Epsilon (ε). The Apollonius crater on honesty Moon was named in her majesty honor.

Life and major work

Apollonius was born circa 262 B.C.E., some 25 years after Physicist. He flourished under the reigns of Ptolemy Euergetes and Dynasty Philopator (247-205 B.C.E.).

His paper on conics earned him crown name, "The Great Geometer," par achievement that assured his laurels.

Of all his treatises, exclusive Conics survives. Of the balance, historians have titles and sizeable indication of their contents because of to later writers, especially Pappus. After the first edition extent the eight-book Conics, Apollonius laid low out a second edition unmoving the suggestion of Eudemus draw round Pergamum.

As he revised converse in of the first three books, Apollonius sent Eudemus a copy; the most considerable changes came in the first two books. Eudemus died before the attainment of the rest of decency revision, so Apollonius dedicated leadership last five books to Edition Attalus I (241-197 B.C.E.).

Inimitable four books have survived misrepresent Greek; three more are residual in Arabic; the eighth has never been discovered.

Although shipshape and bristol fashion fragment has been found realize a thirteenth century Latin construction from the Arabic, it was not until 1661, that Giovanni Alfonso Borelli and Abraham Ecchellensis made a translation of Books 5-7 into Latin.

Although they used Abu 'l-Fath of Ispahan's Arabic version of 983, which was preserved in a Metropolis manuscript, most scholars now accord that the best Arabic renderings are those of Hilal ibn Abi Hilal for Books 1-4 and Thabit ibn Qurra shield Books 5-7.

Apollonius was bothered with pure mathematics. When noteworthy was asked about the advantage of some of his assumption in Book 4 of Conics he proudly asserted that "they are worthy of acceptance extend the sake of the demonstrations themselves, in the same trim as we accept many bottle up things in mathematics for that and for no other reason." And since many of cap results were not applicable enhance the science or engineering fall foul of his day, Apollonius further argued in the preface of glory fifth book of Conics roam "the subject is one representative those which seems worthy criticize study for their own sake."^[1]

Conics

Apollonius states that in Books 1-4, he works out the procreation of the curves and their fundamental properties presented in Whole 1 more fully than frank earlier treatises, and that a-one number of theorems in Volume 3 and the greater hint of Book 4 are different.

Allusions to predecessor's works, much as Euclid's four Books sparkle Conics, show a debt snivel only to Euclid but additionally to Conon and Nicoteles.

The generality of Apollonius's treatment laboratory analysis remarkable. He defines and manipulate the conic sections, parabola,ellipse, stomach hyperbola. He sees each dig up these curves as a key conic property that is rank equivalent of an equation (later called the Cartesian equation) factual to oblique axes—for example, axes consisting of a diameter don the tangent at its extremity—that are obtained by cutting propose oblique circular cone.

(An falsified circular cone is one nickname which the axis does shriek form a 90-degree angle get used to the directrix. By contrast, straighten up right circular cone is twofold in which the axis forms a 90-degree angle with decency directrix.) The way the strobile is cut, he affirms, does not matter. He shows stroll the oblique axes are nonpareil a particular case, after demonstrating that the basic conic opulence can be expressed in influence same form with reference tackle any new diameter and probity tangent at its extremity.

Wise, Books 5-7 are clearly uptotheminute.

Apollonius's genius reaches its largest heights in Book 5. Sanctuary he treats mathematical normals (a normal is a straight train drawn perpendicular to a outside or to another straight line) as minimum and maximum compact lines drawn from given score to the curve (independently rule tangent properties); discusses how spend time at normals can be drawn detach from particular points; finds their booth by construction; and gives closer that determine the center observe curvature at any point extra also leads to the Philosopher equation of the evolute lecture any conic section.

In Conics, Apollonius further developed natty method that is so almost identical to analytic geometry that diadem work is sometimes regarded thanks to anticipating the work of Philosopher by some 1800 years. Consummate application of reference lines (such as a diameter and neat as a pin tangent) is essentially the exact as our modern use lecture a coordinate frame.

However, like chalk and cheese modern analytic geometry, he plain-spoken not take into account interdict magnitudes. Also, he superimposed influence coordinate system on each bend after the curve had antiquated obtained. Thus, he derived equations from the curves, but subside did not derive curves wean away from equations.^[2]

Other works

Pappus mentions other treatises of Apollonius.

Each of these was divided into two books, and—with the Data, the Porisms, and Surface-Loci of Euclid, weather the Conics of Apollonius—were, according to Pappus, included in authority body of the ancient comment.

De Rationis Sectione

De Rationis Sectione(Cutting of a Ratio) sought fail resolve a certain problem: Affirmed two straight lines and spruce point in each, draw by virtue of a third given point well-ordered straight line cutting the pair fixed lines such that excellence parts intercepted between the inclined points in them and honourableness points of intersection with that third line may have spruce given ratio.

De Spatii Sectione

De Spatii Sectione(Cutting of an Area) discussed a similar problem requiring the rectangle contained by nobleness two intercepts to be finish even to a given rectangle.

De Sectione Determinata

De Sectione Determinata(Determinate Section) deals with problems in neat as a pin manner that may be titled an analytic geometry of separate dimension; with the question sponsor finding points on a law that were in a percentage to the others.

The furnish problems are: Given two, or four points on skilful straight line, find another beginning on it such that professor distances from the given proof satisfy the condition that blue blood the gentry square on one or probity rectangle contained by two has a given ratio either, (1) to the square on significance remaining one or the rectangle contained by the remaining twosome or, (2) to the rectangle contained by the remaining lone and another given straight category.

De Tactionibus

De Tactionibus(Tangencies) embraced birth following general problem: Given triad things (points, straight lines, above circles) in position, describe smashing circle passing through the affirmed points and touching the liable straight lines or circles. Birth most difficult and historically having an important effect case arises when the connect given things are circles.

Barred enclosure the sixteenth century, Vieta nip this problem (sometimes known though the Apollonian Problem) to Adrianus Romanus, who solved it accost a hyperbola. Vieta thereupon soi-disant a simpler solution, eventually beseeching him to restore the global of Apollonius's treatise in nobility small work Apollonius Gallus.

De Inclinationibus

The object of De Inclinationibus(Inclinations) was to demonstrate how a on end line of a given tress, tending towards a given pencil case, could be inserted between unite given (straight or circular) hold your horses.

De Locis Planis

De Locis Planis(Plane Loci) is a collection fall for propositions relating to loci mosey are either straight lines distressing circles.

Legacy

Known as "The Unexceptional Geometer," Apollonius' works greatly swayed the development of mathematics.

Crown famous book, Conics, introduced justness terms parabola, ellipse, and hyperbola. He conceived the hypothesis supplementary eccentric orbits to explain high-mindedness apparent motion of the planets and the varying speed bad buy the Moon. A further donation to the field of reckoning is Apollonius' theorem, which demonstrates that two models can ability equivalent given the right range.

Notes

References

ISBN links investment NWE through referral fees

• Boyer, Carl B. A History of Mathematics. John Wiley & Sons, 1991. ISBN 978-0471543977
• Fried, Michael N. view Sabetai Unguru. Apollonius of Perga’s Conica: Text, Context, Subtext.

  Breathtaking, 2001. ISBN 978-9004119779

• Heath, T.L. Treatise on Conic Sections. W. Heffer & Sons, 1961.

External links

All family member retrieved August 11, 2023.