Of the three main styles, French sectors were the most consistent in terms of the scales with which they were marked. They were designed specifically for gunnery rather than for general applications. There were eight common scales:
- Poid des boulets, or weight of artillery shot – Although early modern cannon were not standard in size, there were different types of shot for different general types of artillery. Each type of shot had a particular volume, weight, and amount of powder. This scale helped gunners determine the required weight for a given size of shot.
- Metallic line – The alchemical symbols for certain metals (such as gold, lead, silver, copper, iron, and tin) were placed at distances from the hinge of the sector so that balls of those metals with those radii would weigh the same. The distance between any two metals gave the ratio between their weights.
- Line of solids – Used to determine the ratio between two volumes and to calculate cube roots.
- Line of chords – Used to construct angles.
- Calibre des pieces, or size of artillery shot – This scale was used to determine the size of shot, given the diameter of the cannon opening and the weight of the shot.
- Line of lines – A scale divided into equal parts used as the base scale for taking measurements that are transferred to other scales with a pair of dividers. For example, open the dividers to a length on the line of lines and then pivot the dividers and open the sector so that the lifted point of the dividers falls on the other leg of the sector.
- Line of planes – Used to determine the ratio between two areas and to calculate square roots.
- Tetragonic line – Points placed from the hinge to represent the sides of regular polygons with the same area, from the triangle to a 13-sided polygon. Used to set up proportions to determine the areas of regular polygons with other side lengths.
