🔎 Palimpsest of Archimedes – Definition and Explanations

Introduction

A typical page from the Archimedean palimpsest. The original manuscript of Archimedes’ text was written from right to left, hidden under a prayer text written from top to bottom.

the Archimedes Palimpsest is one of the oldest copies of the work written by mathematician (A mathematician is a researcher in mathematics in a limited sense, in a broad sense…), physicist (A physicist is a scientist who studies the field of physics, ie…) and engineer (The main job of an engineer is to solve the problems of nature…) Greek, Archimedes of Syracuse (287 BC – 212 BC). A palimpsest is a manuscript written on used parchment, the characters of which have been erased in order to reuse the parchment, which was rare and expensive at the time. The original text is by Archimedes (who lived in the 3rd century). century (A century is now a period of one hundred years. The word comes from the Latin word saeculum, i, which…). BC), transferred Xe It was scratched by a priest who rewrote a Greek liturgical book in the 16th century. the second (The second is the feminine of the second adjective immediately following the first, or which…) half of it XIIe century or the first half XIIIe century

The Archimedean Palimpsest is bound as a codex. It was about a 90-page book before it became a 177-page palimpsest. Fortunately, the erasure of the original text was not complete and thanks to ultraviolet light, it can still be read. x-ray (X-rays are a form of high-frequency electromagnetic radiation…) and just light (Light is a collection of visible electromagnetic waves…).

Discovered in Constantinople in 1906 and published from photographs by the Danish philologist Johan Ludwig Heiberg (1854-1928); then translated from the Greek into English by Thomas Heath. Among the texts of Archimedes included in the work, it allowed society scientist (A scientist dedicated to the study of a science or sciences and…) to discover some never before published:

  • In the balance of plane figures
  • Spirals.
  • From the size of the circle.
  • From the globe and cylinder (A cylinder is a surface defined by a straight line (d) in space, called…)
  • floaters (Only known copy in Greek)
  • From the method (known copy only)
  • Stomach (known copy only)

The palimpsest also contains speeches by the 4th century BC politician Hyperides and commentaries on the Categories.Aristotle (Aristotle (in ancient Greek…) By Alexander of Aphrodisias.

Mathematics content

Method

The most notable content of this palimpsest is the treatise Archimedes Method is its only known copy. This treatise provides valuable information about the method used by Archimedes to determine certain dimensionsfield (Aires (Spanish for air) is Colombia’s domestic airline.) or volume (In physics or mathematics, volume is a quantity that measures expansion…)for example, the area of ​​a segment proverb (A parabola is the intersection of a plane and a cone when the plane is parallel…) or the volume of the ball. In addition to these two results, there is also the calculation Center of gravity (The center of gravity is the point of application of forces resulting from…) of the hemisphere and a body (Can be luggage 🙂 of paraboloid (In mathematics, a paraboloid is a quadratic surface of Euclidean space. It is…).

Geometrical proofs of the area or volume formula have been known since antiquity and are based on an absurd dual reasoning called the method of exhaustion: to prove that two quantities are equal, we show that the first is greater than the second, leading to a contradiction (Contradiction occurs when two statements, ideas, or actions are mutually exclusive.), then we assume that the second is greater than the first to reach another contradiction. Then we deduce the equality of the two quantities. These considerations are generally based on framing the figure with increasingly precise square figures (see squaring the parabola). However, the exhaustion method requires a priori knowledge of the final result. For example, the area of ​​a parabola segment is not calculated; we prove that this area is equal to 4/3 of a certain area triangle (In Euclidean geometry, a triangle is a plane figure formed by three points…) given in this segment. Similarly, the volume of the ball is not calculated; we prove that this volume is four times the volume of the cone with base aa large circle (In geometry, a great circle is a circle drawn on the surface of an identical sphere…) ball and height (Height has several meanings depending on the subject area.) is equal to the radius of the ball. But we didn’t know how Archimedes was able to guess which formulas to prove. It is in the explanation Method.

In this treatise, Archimedes uses mechanical methods by cutting volumes calculated on scales, surfaces, or slices (see squares by weight method). His approach is notable for its unique use at the timeinfinity (The word “infinity” (-e, -s; Latin finitus,…)It uses techniques very close to techniques that would be reinvented in the 17th century, especially Cavalieri’s method of indivisibles. integral calculus (Integral calculus is the second idea of ​​infinitesimal calculus.) Newton and Leibniz. None of these authors knew Method It was used by Archimedes.

A few pages Method was not used by the author of the palimpsest and is therefore permanently lost, as is the calculation of the volume of the intersection of two cylinders.

Stomach

the Stomach It is a puzzle problem that exists in Archimedes’ Palimpsest

Palimpsest is an example of this Stomach : this challenge is presented as a jigsaw puzzle. Similar to a tangram, it has 14 pieces (versus 7 for a tangram). the document (In its current sense, a document is generally defined as the physical support of a…) It is very incomplete with regard to the stomach, but Archimedes gives the method of its construction, and the proportions of the various parts, as well as of the angles of its areas. Reviel NetzStanford University (Leland Stanford Junior University, better known as Stanford University, is one…) I think it is about the thought of Archimedes number (The concept of number in linguistics is considered in the article “Number…”) ways of reconstruction. Calculations on the combinations lead to 17,152 possible combinations, of which 536 are different. isometric (In geometry, an isometry is a transformation that preserves lengths. An isometry…) enables close reconstruction square (A square is a regular polygon with four sides. This means that its…). The document in the palimpsest is too incomplete to know whether Archimedes reached the same conclusion. This work would then be of the most perfect use combinatorial (In mathematics, combinatorics is also called combinatorial analysis…) in ancient greek.

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