Book:Euclid/The Elements/Book I

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Euclid: The Elements: Book I

Published $c. 300 B.C.E$.


Contents

Book $\text{I}$: Straight Line Geometry

Definitions
Postulates and Common Notions
Proposition $1$: Construction of Equilateral Triangle
Proposition $2$: Construction of Equal Straight Line
Proposition $3$: Construction of Equal Straight Lines from Unequal
Proposition $4$: Triangle Side-Angle-Side Equality
Proposition $5$: Isosceles Triangle has Two Equal Angles
Proposition $6$: Triangle with Two Equal Angles is Isosceles
Proposition $7$: Two Lines Meet at Unique Point
Proposition $8$: Triangle Side-Side-Side Equality
Proposition $9$: Bisection of Angle
Proposition $10$: Bisection of Straight Line
Proposition $11$: Construction of Perpendicular Line
Proposition $12$: Perpendicular through Given Point
Proposition $13$: Two Angles on Straight Line make Two Right Angles
Proposition $14$: Two Angles making Two Right Angles make Straight Line
Proposition $15$: Two Straight Lines make Equal Opposite Angles
Proposition $16$: External Angle of Triangle Greater than Internal Opposite
Proposition $17$: Two Angles of Triangle Less than Two Right Angles
Proposition $18$: Greater Side of Triangle Subtends Greater Angle
Proposition $19$: Greater Angle of Triangle Subtended by Greater Side
Proposition $20$: Sum of Two Sides of Triangle Greater than Third Side
Proposition $21$: Lines Through Endpoints of One Side of Triangle to Point Inside Triangle is Less than Sum of Other Sides
Proposition $22$: Construction of Triangle from Given Lengths
Proposition $23$: Construction of Equal Angle
Proposition $24$: Hinge Theorem
Proposition $25$: Converse Hinge Theorem
Proposition $26$: Triangle Angle-Side-Angle and Side-Angle-Angle Equality
Proposition $27$: Equal Alternate Interior Angles implies Parallel Lines
Proposition $28$: Equal Corresponding Angles or Supplementary Interior Angles implies Parallel Lines
Proposition $29$: Parallelism implies Equal Alternate Interior Angles, Corresponding Angles, and Supplementary Interior Angles
Proposition $30$: Parallelism is Transitive
Proposition $31$: Construction of Parallel Line
Proposition $32: \text{ Part } 1$: External Angle of Triangle equals Sum of other Internal Angles
Proposition $32: \text{ Part } 2$: Sum of Angles of Triangle equals Two Right Angles
Proposition $33$: Lines Joining Equal and Parallel Straight Lines are Parallel
Proposition $34$: Opposite Sides and Angles of Parallelogram are Equal
Proposition $35$: Parallelograms with Same Base and Same Height have Equal Area
Proposition $36$: Parallelograms with Equal Base and Same Height have Equal Area
Proposition $37$: Triangles with Same Base and Same Height have Equal Area
Proposition $38$: Triangles with Equal Base and Same Height have Equal Area
Proposition $39$: Equal Sized Triangles on Same Base have Same Height
Proposition $40$: Equal Sized Triangles on Equal Base have Same Height
Proposition $41$: Parallelogram on Same Base as Triangle has Twice its Area
Proposition $42$: Construction of Parallelogram equal to Triangle in Given Angle
Proposition $43$: Complements of Parallelograms are Equal
Proposition $44$: Construction of Parallelogram on Given Line equal to Triangle in Given Angle
Proposition $45$: Construction of Parallelogram in Given Angle equal to Given Polygon
Proposition $46$: Construction of Square on Given Straight Line
Proposition $47$: Pythagoras's Theorem
Proposition $48$: Square equals Sum of Squares implies Right Triangle