Which of the following tools did the Greeks limit themselves to in their formal geometric constructions?

The Greeks limited themselves to two tools in their formal geometric constructions: a straightedge and a compass.

1. Straightedge: This tool, also known as a ruler, was used to draw straight lines. However, the Greeks used it without measurement markings, meaning it was used only to draw lines through given points or to extend existing lines.

2. Compass: This tool was used to draw circles and arcs. The Greeks used a collapsing compass, meaning it could not be used to transfer lengths.

These limitations led to certain restrictions in Greek geometry. For example, they could only construct lengths or angles that were the result of a finite sequence of these basic operations. This is why problems like trisecting an angle or doubling a cube, which require more complex operations, were impossible for them to solve using these tools alone.