[1]. The intersections of two straight lines make four angles, of which those that are opposite are always equal to one another.

2. Two straight lines intersecting at the centre of the circle will cut that circle so that the opposite parts are equal to one another.

3. If equal angles have their sides equal, then their third sides too will be equal to one another.

4. All the straight lines that extend between the centre and the circumference are equal to one another.

5. If from equal things equal parts are taken away, the remainder will stay equal.

6. The circles that are drawn on one and the same centre will all exceed one another by parallel spaces.

1. Given the visible object and the eye, one asks for the place where that object will appear on the plane mirror.

2. Given the place where the visible object appears, one asks for the position of the true object and the position of the eye.

3. Given the eye and the image, one seeks the origin of the line of the image.

4. Given the visible object and the image, one asks for the position of the line of the eye.

And what is here said of the plane mirror is understood also of convex mirrors and of concave mirrors.

Given the luminous body and the eye, let it be sought to find where the greatest light will be upon the spherical body.

Given the greatest light found upon the spherical body, let the lines of the light and of the eye be investigated.

Given the light and its image, the line of the eye is sought.

Given the eye and the image, the line of the light is sought.

a - b (m) - u t - d o - x c S - y r - e m d - f

Let a be the luminous body, and d c e be the mirror. I say then that c is the place of the greatest light. It is proved by the circle t u: and by the first proposition the angles o d are equal to one another; and by the second the curved bases t r and u y are also equal to one another.

And by the sixth proposition the excess of the two circles drawn on one and the same centre f is parallel, that is, of equal width.

And by the fifth proposition the parts taken from the two triangles t r o and d u x are equal.

a d - m c n - c e

This will be the converse of the one above, that is, upside-down of the one above.

From the given points of the luminous body and of the eye it is possible to find the length of the reflected ray and of the incident ray. Given the point that ends the incident ray and causes the reflected ray, you will never find the length of the lines, that is, of the incident and the reflected ray.