# Euclidean geometry

early example of an axiomatic structure in mathematics. Nowadays, all of conventional mathematics is formalized by mathematical logic and ZFC. However, Euclid axiomatized geometry and number theory completely separately because he did not have the abstractions available to us today.
extended by cartesian geometry
- point
- line
- plane
- space
- angle
- distance
- parallel lines
- perpendicular lines

- triangle
- scalene triangle
- isoceles triangle
- right angled triangle


- square
- rhombus
- rectangle
- parallelogram

- circle
- polygon

-congruent figures


- ellipse
- focus
- locus

- diameter
- radius
- chord
- arc
- segment
- tangent
- secant


- Pythagorean theoem
- isosceles triangle theorem (pons asinorum)
- triangle angle sum theorem
- polygon angle sum theorem
- angle sum theorem
- Thale's theorem
- inscribed angle theorem
- alternate segment theorem
- intersecting chords theorem
- ptolemy's theorem




3. Trigonometry
\chapter{Trigonometric functions}
\section{Congruence between right angle triangles}
\section{Trigonometric functions}
- sine
- cosine
- tangent
\section{Recirpocal trigonometric functions}
- cosecant
- secant
- cotangent

\chapter{Inverse trigonometric functions}
\chapter{Inverse trigonometric functions}
- cosecant
- secant
- cotangent
\chapter{Inverse trigonometric functions}


\chapter{Theorems of trigonometry}

- sine rule
- cosine rule

-radians
-
 
\section{Further properties of trigonometric functions}

\[\sin (\theta) = \cos (\pi - \theta)\]




\[\sin^2 (\theta) + \cos^2 (\theta) = 1\]
\[ 1 + \cot^2 (\theta) = \sec^2 (\theta)\]
\[\sin(\theta + \phi) = \sin(\theta) \cos(\phi) + \sin(\phi) \cos(\theta) \]
\[\cos(\theta + \phi) = \cos(\theta) \cos(\phi) - \sin(\phi) \sin(\theta) \]


\[\sin(2\theta ) = 2\sin(\theta) \cos(\theta) \]
\[\cos(2\theta ) = \cos^2 (\theta) - \sin^2 (\theta) \]

4. Compass & straightedge constructions
Compass equivalence theorem
Mohr-Mascheroni theorem
Poncelet-Steiner theorem