Euclid used deductive reasoning to prove his Optics theorems. Deductive reasoning is basically using many statements is a sort of 'top-down' logic to prove theorems.
Now what Euclid did in Opticswas that he used many postulates and definitions to prove the theorems about vision.
Some of the postulates in Optics are:
Let it be assumed :
1. That rectilinear rays proceeding from the eye diverge indefinitely;
2. That the figure contained by a set of visual rays is a cone of which the vertex is at the eye and the base at the surface of the objects seen;
3. That those things are seen upon which visuals rays fall and those things are not seen upon which visual rays do not fall;
4. That things seen under a larger angle appear larger, those under a smaller angle appear smaller, and those under equal angles appear equal;
5. That things seen by higher visual rays appear higher, and things seen by lower visual rays appear lower;
6. That, similarly, things seen by rays further to the right appear further to the right, and things seen by rays further to the left appear further to the left;
7. That thing seen under more angles are seen more clearly.
Using these postulates, Euclid proved his theorems about optics. This methodology is called Deductive Reasoning.