How did the Romans build straight roads that stretched very long distances?

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The simple answer is that they used a form of surveying tool called a groma. This basically consisted of two pieces of wood nailed together to form a square cross with right angles in all corners. Each piece of wood had lead weights attached to the end, and they determined they had a straight line when the lead weight from one piece of wood lined up with the one in front of it. Wood posts would be used to stake out the boundaries of the road in order to help maintain a straight line over an extended distance.

As an interesting side note, I found another source that indicated that Roman soldiers carried a tool such as a hatchet, pick, or spade in addition to his more traditional gear. When there was a need to build roads, the engineers would take groups of soldiers to use as laborers. This served a dual purpose of keeping the men in shape while also keeping them out of trouble.

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Here is an interesting and well-cited article from Ferris State University College of Technology Surveying Engineering (there's a name that flows from the tongue) covering the technical aspects of ancient Roman surveying techniques.

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