Book:Euclid/The Elements/Book V

As Augustus De Morgan put it:
 * ...simple propositions of concrete arithmetic, covered in languaqe which makes them unintelligible to modern ears.

Contents

 * Book V: Theory of Proportions
 * Definitions
 * Proposition 1: Multiplication of Numbers Distributes over Addition (1)
 * Proposition 2: Multiplication of Numbers Distributes over Addition (2)
 * Proposition 3: Multiplication of Numbers is Associative
 * Proposition 4: Multiples of Terms in Equal Ratios
 * Propositions 5 and 6: Multiplication of Numbers Distributes over Subtraction‎
 * Proposition 7: Ratios of Equal Magnitudes
 * Proposition 8: Relative Sizes of Ratios on Unequal Magnitudes
 * Proposition 9: Magnitudes with Same Ratios are Equal
 * Proposition 10: Relative Sizes of Magnitudes on Unequal Ratios
 * Proposition 11: Equality of Ratios is Transitive
 * Proposition 12: Sum of Components of Equal Ratios
 * Proposition 13: Relative Sizes of Proportional Magnitudes
 * Proposition 14: Relative Sizes of Components of Ratios
 * Proposition 15: Ratio Equals its Multiples
 * Proposition 16: Proportional Magnitudes are Proportional Alternately
 * Proposition 17: Magnitudes Proportional Compounded are Proportional Separated
 * Proposition 18: Magnitudes Proportional Separated are Proportional Compounded
 * Proposition 19: Proportional Magnitudes have Proportional Remainders
 * Proposition 20: Relative Sizes of Successive Ratios