Description: Dioptra
Image copyright: http://surveyingeospatial.blogspot.com/2009/05/historythe-dioptra.html
The dioptra was used manly as a level, measuring distance and angles. This instrument is very complex, so this was only used over long distances because that is where it is more accurate. They used this tool for celestial observations. This instrument is the image above.
The decempeda was just a gaint ruler that measured land. It was 10 foot long and made out of hardwood like oak, with caps of bronze on either end so two of them can be put together.
The groma was used just for laying out straight lines and right angles over large distances, like roads.