Euclid of Alexandria (365? - 275? BC). Little is known of Euclid’s life. The exact dates of his birth and death (as well as his birthplace and nationality) are unknown. Euclid is remembered mainly for his monumental work, entitled Elements, which was essentially a compilation of the mathematics of the classical Greek period that preceded him. This massive work comprised 13 books and contained 465 propositions. Elements emphasized the discipline of mathematics as a deductive science based on explicit axioms and, as such has influenced the course of mathematics as has no other work. While much of Elements was devoted to geometry, Books VII-IX as well as portions of Book X were devoted to the theory of numbers. It is Euclid’s proof of the
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A point is that which hath no parts, or which hath no magnitude.
II. A line is length without breadth.
III. The extremities of a line are points.
IV. A straight or right line is that which lies evenly between its extremities.
V. A surface is that which has length and breadth only. …
Who could fail to follow this logical progression? And who has never heard of the so-called Pythagorean Theorem, which is introduced as the 47th theorem in Euclid’s First Book of Elements? But everything suddenly appears much more difficult and more demanding when one has left the explanations of simple figures behind and is confronted by the doctrine of proportions in the Fifth Book or, before that, by the challenging theorems about parallels and their behavior in infinity which were rediscovered at the beginning of non-Euclidian geometry:
Francesco Barozzi wrote in 1560 that Euclid had shaped the science of mathematics according to rules of both the utmost order and the highest artistry. Generously interpreted, this means that Euclid’s Elements is actually a ‘work of art’, inspiring awe and marvel. Centuries later, Albert Einstein in Geometry and Experience (1921) was puzzled and prompted by the “riddle” to wonder why “mathematics, which is a product of human thought and independent of all experience, so excellently fits real …show more content…
This equally well describes the cultural-historical context in which Euclid had come to occupy his precise locus.
A point is that which hath no parts, or which hath no magnitude.
II. A line is length without breadth.
III. The extremities of a line are points.
IV. A straight or right line is that which lies evenly between its extremities.
V. A surface is that which has length and breadth only. …
Who could fail to follow this logical progression? And who has never heard of the so-called Pythagorean Theorem, which is introduced as the 47th theorem in Euclid’s First Book of Elements? But everything suddenly appears much more difficult and more demanding when one has left the explanations of simple figures behind and is confronted by the doctrine of proportions in the Fifth Book or, before that, by the challenging theorems about parallels and their behavior in infinity which were rediscovered at the beginning of non-Euclidian geometry:
Francesco Barozzi wrote in 1560 that Euclid had shaped the science of mathematics according to rules of both the utmost order and the highest artistry. Generously interpreted, this means that Euclid’s Elements is actually a ‘work of art’, inspiring awe and marvel. Centuries later, Albert Einstein in Geometry and Experience (1921) was puzzled and prompted by the “riddle” to wonder why “mathematics, which is a product of human thought and independent of all experience, so excellently fits real …show more content…
This equally well describes the cultural-historical context in which Euclid had come to occupy his precise locus.