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!)