Euclid | Archimedes | Apollonius of Perga | Nicomachus

by Euclid, Archimedes, Nicomachus

Contains the 13 books of Euclid's Elements, the works of Archimedes including the Method, the Conics of Apollonius of Perga, and the Introduction to Arithmetic of Nicomachus of Gerasa.

Genres: Mathematics, Science, Philosophy, Classics

848 pages, Hardcover

First published January 1, 1952

About the author

Euclid (Ancient Greek: Εὐκλείδης Eukleidēs -- "Good Glory", ca. 365-275 BC) also known as Euclid of Alexandria, was a Greek mathematician, often referred to as the "Father of Geometry". He was active in Alexandria during the reign of Ptolemy I (323–283 BC). His Stoicheia (Elements) is a 13-volume exploration all corners of mathematics, based on the works of, inter alia, Aristotle, Eudoxus of Cnidus, Plato, Pythagoras. It is one of the most influential works in the history of mathematics, presenting the mathematical theorems and problems with great clarity, and showing their solutions concisely and logically. Thus, it came to serve as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In the Elements, Euclid deduced the principles of what is now called Euclidean geometry from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor. He is sometimes credited with one original theory, a method of exhaustion through which the area of a circle and volume of a sphere can be calculated, but he left a much greater mark as a teacher.

Reviews

[Michael Greer · Rating 5 out of 5]

This volume is perhaps the best place to start for beginners in Greek mathematics. Plato was known to have demanded each student be competent in geometry before beginning the hard work of the philosopher. Unlike many ancient Christians I am less suspicious of so-called "pagan authors," and this volume represents the best reason why. Clarity, demonstration, reasoning also belong to all those who adhere to monotheism. We ought not to dismiss Plato simply because he lived and worked during a time of polytheistic ritual practice. Geometry may be the best exercise for converting mere readers into reflective people and then into philosophers (in other words, people with free and open minds). This progression is a form of conversion but probably better represented as a development. Many people read for simple emotional reasons, stimulating the imagination as an escape. Those trained to reflect as readers are more likely to hunger for reality. Mathematics can assist those who seek reality.

[Eric Farnsworth · Rating 3 out of 5]

Euclid book 2-6 only

[Paul · Rating 4 out of 5]

Even if you're a trained mathematician, to read this work carefully and with full comprehension would be a years-long project. Not that the math in it is especially difficult: if you've got mathematical aptitude and did well in high-school math, then you'll be able to understand the proofs. But there are so many of them! And they are presented in such a compressed style (especially Archimedes'). Nonetheless, this book shows you exactly what the best mathematical minds of the Hellenistic world were occupied with, and the many conclusions they were able to develop.

I guess I would say that this volume can be scanned, with profit, at different speeds by different readers.

[Sarah · Rating 4 out of 5]

I read the following: Archimedes' The Sand-Reckoner, On the Equilibrium of Planes, and On Floating Bodies.

These were short but hard to understand. With external commentaries, I was able to get a decent understanding of their main points. I'm impressed by his genius and reminded that I will never be a mathematician!

[Christopher Rush · Rating 2 out of 5]

This must have been before numbers were invented. Apparently back then you could prove your mathematical postulates by saying, "Draw lines and curves in a way that proves I'm right. See? I'm right." It must have been an exciting time to be alive.

[William Crosby]

I looked at every page, but did not study the propositions and lemmas. I.e. I skimmed rather than read or studied this book. Lots of formulas and diagrams.