Geometry Mastering Magnitudes Elements Commentary

Euclid geometry

Geometry

The character known as Euclid, or Eukleidēs in the Greek, wrote the textbook on mathematics, laying out a system based on definitions and axioms, each theorem rigorously proven, that established the logic that all educated people studied for twenty-three centuries.

Mastering

Euclid took from Plato the use of definitions and axioms, reworked theorems by Eudoxus of Cnidus, perfected theorems by Theaetetus, based the books of his Elements on Pythagoras of Samos, Hippocrates of Chios, and other Pythagorean or Athenian mathematicians, but Euclid worked his borrowings into a comprehensive deductive system with his own rigorous proofs so that today his name is synonymous with . . . uh . . . Euclidean geometry.

Magnitudes

Euclid measured a line only in relation to the length of another line. He measured an angle only in relation to the perpendicular. He used positive numbers and fractions; negative numbers were not geometrically meaningful. Multiplication of two lengths produced an area. Numbers were more understandable as geometric quantities than as Alexandrian numerals.

Elements

Letters (elements in the Greek) label points in the diagrams so that the text can simply reference them.

1. That the signifier is not the signified dissolves in memory.
2. Etymology persists as meaning.
3. Your name becomes you.
4. A smell can evoke everything.

• When the magician or comedian points,
• pay attention to the end of his finger.
• (Ha ha. Just kidding!)