Frases de Pappus de Alejandría

Papo de Alejandría fue uno de los últimos grandes matemáticos griegos de la Antigüedad, conocido por su obra Synagoge . Apenas se sabe nada de su vida, más que fue maestro en Alejandría y que tuvo un hermano llamado Hermodoro.

Su Synagoge , es su obra mejor conocida. Es un compendio de matemáticas de ocho volúmenes. Trata de una gran variedad de problemas de geometría, matemática recreativa, duplicado del cubo, polígonos y poliedros.

Pappus vivió en la primera mitad del siglo IV. Su figura sobresale del estancamiento general de la matemática de su época.[1]

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La Synagoge fue traducida al latín en 1588 por Federico Commandino. El historiador de la matemática y clasicista Friedrich Hultsch publicó en 1878 la versión definitiva en griego y latín de Papus. Paul Ver Eecke, historiador belga, tradujo la obra al francés en 1933.[2]

En geometría, se le atribuyen varios teoremas, conocidos todos con el nombre genérico de Teorema de Pappus. Entre éstos están:

Teorema del centroide de Pappus,

La cadena de Pappus,

Teorema armónico de Pappus

Teorema del hexágono de Pappus. Wikipedia

✵ 290 – 350

Pappus de Alejandría Foto

Pappus de Alejandría: 5 frases 0 Me gusta

Pappus de Alejandría: Frases en inglés

“The so called άναλυόμϵνος ('Treasury of Analysis') is… a special body of doctrine provided for the use of those who, after finishing the ordinary Elements, are desirous of acquiring the power of solving problems which may be set them involving (the construction of) lines, and it is useful for this alone. It is the work of three men, Euclid the author of the Elements, Apollonius of Perga, and Aristaeus the elder, and proceeds by way of analysis and synthesis.”

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Pappus of Alexandria

Fuente: The Thirteen Books of Euclid's Elements (1908), Ch. IX. §6

“He [Apollonius of Perga] spent a very long time with the pupils of Euclid at Alexandria, and it was thus that he acquired such a scientific habit of thought.”

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Pappus of Alexandria

Fuente: The Thirteen Books of Euclid's Elements (1908), Ch. 1, p.2

“But in synthesis, reversing the process, we take as already done that which was last arrived at in the analysis and, by arranging in their natural order as consequences what were before antecedents, and successively connecting them one with another, we arrive finally at the construction of what was sought; and this we call synthesis.”

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Pappus of Alexandria

Fuente: The Thirteen Books of Euclid's Elements (1908), Ch. IX. §6

“Now analysis is of two kinds, the one directed to searching for the truth and called theoretical, the other directed to finding what we are told to find and called problematical. (1) In the theoretical kind we assume what is sought as if it were existent and true, after which we pass through its successive consequences, as if they too were true and established by virtue of our hypothesis, to something admitted: then (a), if that something admitted is true, that which is sought will also be true and the proof will correspond in the reverse order to the analysis, but (b), if we come upon something admittedly false, that which is sought will also be false. (2) In the problematical kind we assume that which is propounded as if it were known, after which we pass through its successive consequences, taking them as true, up to something admitted: if then (a) what is admitted is possible and obtainable, that is, what mathematicians call given, what was originally proposed will also be possible, and the proof will again correspond in reverse order to the analysis, but if (b) we come upon something admittedly impossible, the problem will also be impossible.”

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Pappus of Alexandria

Fuente: The Thirteen Books of Euclid's Elements (1908), Ch. IX. §6

“Analysis… takes that which is sought as if it were admitted and passes from it through its successive consequences to something which is admitted as the result of synthesis: for in analysis we assume that which is sought as if it were (already) done (ɣϵɣονός) and we inquire what it is from which this results, and again what is the antecedent cause of the latter, and so on, until by so retracing our steps we come upon something already known or belonging to the class of first principles, and such a method we call analysis as being solution backwards”

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Pappus of Alexandria

άνάπαλɩν λὐσɩν
The Thirteen Books of Euclid's Elements (1908)