Mathematics: Running fixes

The sum of angles in a triangle is 180°

Draw a triangle ABC, then draw a line DAE parallel to line BC.
Now, angles α and β in the triangle equal angles DAB and EAC, respectively.
Therefore, the sum of angles in the triangle is 180° : a straight line.

“Doubling the angle” yields two equal angles

So, α + δ + γ = 180°
α + 180 − β + γ = 180°
2α = β
α + 180 − 2α + γ = 180°
180° − α + γ = 180°
−α + γ = 0
γ = α

Two equal angles render an triangle isosceles

In the triangle aboveon the right, α = γ and β = 2α.
By constructing the bisector h of angle β we create two little triangles in which x = y.
Therefore, d₁ = d₂.

Next math chapter: Distance of horizon,
or back to chapter 5 of the navigation course,
or (learn to) sail (bareboat or in flotillas) in Greece and beyond…