Calculating the distance of a ship from the shore

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Calculating the distance of a ship from the shore


From the point of the shore which is found opposite the ship, we cover (perpendicularly) at length of the shore a random distance (eg 20 steps) where we place a stick and at its extension we cover an equal distance (of 20 steps). Afterwards, we walk (perpendicularly) inland up to the point where we can aim the ship through our stick. Then (due to the shaping of two equal triangles) our distance from the shore equals the requested distance of the ship from the shore. This method, which is attributed to Thales of Miletus, was also used to find the width of a river, α cliff, etc.

SOURCES: "Proklos Diadochos, A Commentary on the First Book of Euclid's Elements"