Euclid's Elements Book II

graph TD BookI["Book I\nFoundation"] Def1["Def. II.1\nRectangle contained by two strai..."] Def2["Def. II.2\nGnomon: parallelogram about diam..."] Prop1["Prop. II.1\nRectangle = sum of rectangles"] Prop2["Prop. II.2\nSum of rectangles = square on whole"] Prop3["Prop. II.3\nRectangle = rectangle + square"] Prop4["Prop. II.4\nSquare on whole = squares + 2×rectangle"] Prop5["Prop. II.5\nUnequal segments: rectangle + square = square on half"] Prop6["Prop. II.6\nBisected + added: rectangle + square = square"] Prop7["Prop. II.7\nSquare on whole + square on segment"] Prop8["Prop. II.8\nFour times rectangle + square"] Prop9["Prop. II.9\nUnequal segments: sum of squares"] Prop10["Prop. II.10\nBisected + added: sum of squares"] Prop11["Prop. II.11\nCut line: rectangle = square (golden section)"] Prop12["Prop. II.12\nObtuse triangle: law of cosines"] Prop13["Prop. II.13\nAcute triangle: law of cosines"] Prop14["Prop. II.14\nConstruct square = rectilinear figure"] BookI --> Prop1 Def1 --> Prop1 BookI --> Prop2 Def1 --> Prop2 BookI --> Prop3 Def1 --> Prop3 BookI --> Prop4 Def1 --> Prop4 BookI --> Prop5 Def1 --> Prop5 Def2 --> Prop5 BookI --> Prop6 Def1 --> Prop6 Def2 --> Prop6 BookI --> Prop7 Def1 --> Prop7 BookI --> Prop8 Def1 --> Prop8 BookI --> Prop9 Def1 --> Prop9 BookI --> Prop10 Def1 --> Prop10 BookI --> Prop11 Prop6 --> Prop11 BookI --> Prop12 Prop4 --> Prop12 BookI --> Prop13 Prop7 --> Prop13 BookI --> Prop14 Prop5 --> Prop14 classDef foundation fill:#95a5a6,color:#fff,stroke:#7f8c8d classDef definition fill:#b197fc,color:#fff,stroke:#9775fa classDef proposition fill:#51cf66,color:#fff,stroke:#40c057 class BookI foundation class Def1,Def2 definition class Prop1,Prop2,Prop3,Prop4,Prop5,Prop6,Prop7,Prop8,Prop9,Prop10,Prop11,Prop12,Prop13,Prop14 proposition