Euclid's Elements Book I — Propositions 1–5

graph TD Def15["Def. 15\nCircle — plane figure,\nequal lines from center"] Def20["Def. 20\nTriangle — equilateral,\nisosceles, scalene"] P1["Post. 1\nDraw a straight line\nbetween two points"] P2["Post. 2\nExtend a straight line\ncontinuously"] P3["Post. 3\nDraw a circle with given\ncenter and radius"] CN1["CN 1\nThings equal to the same\nthing are equal to each other"] CN3["CN 3\nIf equals subtracted from\nequals, remainders are equal"] CN4["CN 4\nThings coinciding with\none another are equal"] CN5["CN 5\nThe whole is greater\nthan the part"] Prop1["Prop. I.1\nConstruct an equilateral\ntriangle on a given line"] Prop2["Prop. I.2\nPlace a line segment equal\nto a given segment at a point"] Prop3["Prop. I.3\nCut off from the greater of\ntwo lines a segment equal to the less"] Prop4["Prop. I.4\nSAS Congruence:\ntwo triangles with two equal sides\nand included angle are congruent"] Prop5["Prop. I.5\nBase angles of an\nisosceles triangle are equal"] Def15 --> Prop1 Def20 --> Prop1 Def15 --> Prop2 Def20 --> Prop5 P1 --> Prop1 P3 --> Prop1 Prop1 --> Prop2 P1 --> Prop2 P2 --> Prop2 P3 --> Prop2 Prop2 --> Prop3 P3 --> Prop3 CN4 --> Prop4 CN5 --> Prop4 Prop1 --> Prop5 P1 --> Prop5 P2 --> Prop5 CN1 --> Prop5 CN3 --> Prop5 Prop4 --> Prop5 classDef definition fill:#b197fc,color:#fff,stroke:#9775fa classDef postulate fill:#ff6b6b,color:#fff,stroke:#c0392b classDef commonnotion fill:#ffd43b,color:#000,stroke:#f59f00 classDef proposition fill:#51cf66,color:#fff,stroke:#40c057 class Def15,Def20 definition class P1,P2,P3 postulate class CN1,CN3,CN4,CN5 commonnotion class Prop1,Prop2,Prop3,Prop4,Prop5 proposition