كتاب المناظر (The Optics of Ibn al-Haytham, Books I-III)

not have been properly placed. If the latter is the case, he should alter the circle and examine it with his eye until it is precisely placed — that is, until he finds that by moving his eye round the hole’s circumference he will see the circumference of the circle and nothing beyond it.

2a[56] When this circle has been precisely placed, | let him turn to the inclined hole and, placing his eye at its circumference, look at the white wall. He will perceive the circle drawn on this wall and its circumference and nothing more. Further, if he moves his eye round the circumference of the inclined hole, while looking at the farthest perceptible point on the wall, he will perceive the circle and its circumference and nothing more, or less.

[57] For the ratio of the line between the centres of the two far circles on the interior surface of the wooden block

to the line between the centres of the two opposite circles on the exterior surface,
is as the ratio of the line extending along the axis of the perpendicular hole between the centre of the interior circle and the surface of the white wall
to the part of this line between the two walls.

[58] Then, the axis of the inclined hole, if produced, will meet the axis of the perpendicular hole at the same point in which the latter axis meets the surface of the white wall.

2b[59] But the centre of the circle | drawn on the white wall is the point at which the axis of the perpendicular hole meets the surface of the white wall.

[60] Therefore, the axis of the inclined hole, if produced, will meet the surface of that wall at the centre of the circle drawn on it.

[61] This being so,

the ratio of the line between the centre of the circle drawn on the surface of the wall and the middle of the axis of the inclined hole
to the remaining half of this axis,
is as the ratio of the line between the centre of the said circle and the middle of the axis of the perpendicular hole
to the remaining half of this axis — for the line joining the mid-points of the two axes is parallel to the line joining the centres of the two circles.

[62] And this ratio is the ratio of the radius of the circle drawn on the wall to the radius of the circle of the perpendicular hole inside the chamber — for

the circumference of the circle drawn on the wall is visible from the circumference of this hole;
and nothing can be perceived by the eye except along straight lines;
and, therefore, the eye will perceive the circumference of the circle
3aon the wall along the straight lines | passing through the diagonally opposed points on the circumferences of the two circles of the hole and ending at the circumference of the circle on the wall;

again, the eye perceives the circumference of the circle on the wall from all points on the circumference of the circle of the perpendicular hole;
therefore, all the straight lines passing through the circumferences of the two circles belonging to the perpendicular hole and through the circumference of the circle on the wall will intersect at the middle of the axis of this hole —
since the two circles belonging to the hole are equal and since the diagonal lines intersect at the middle of the hole’s axis.

[63] Consequently,

the ratio of the line between the centre of this drawn circle on the wall and the middle of the axis of the perpendicular hole
to half this axis,
is as the ratio of the radius of the circle on the wall
to the radius of the interior circle of the hole.

[64] But the ratio of the line between the centre of the circle drawn on the wall and the middle of the axis of the perpendicular hole

to half this axis,
is as the ratio of the line between the centre of the circle on the wall and the middle of the axis of the inclined hole
to half this axis.

I 43b[65] Therefore,

the ratio of the line between the centre | of the circle on the wall and the middle of the axis of the inclined hole
to half this axis,
is as the ratio of the radius of the circle drawn on the wall
to the radius of the interior circle of the inclined hole —
since the circle belonging to the inclined hole is equal to that which belongs to the perpendicular hole.

[66] This being so the case, the most that can appear to the eye on the surface of the wall, while the eye is at the circumference of the inclined hole, is the circumference of the circle drawn on that wall opposite the perpendicular hole.

[67] If the experimenter, when his eye is at the circumference of the inclined hole, perceives something of the wall outside the circle, this will be either because the surface of the wooden block is not parallel to the wall’s surface, or because the distance between the block and the wall is not the same as that according to which the line on the surface of the block has been divided. If that is the case he should adjust the position of the wooden block and look through the perpendicular and the inclined hole, until the block is properly placed and all he sees through both holes is nothing more or less than the circle drawn on
I 44athe wall’s surface. For if the wooden block has been precisely placed, | the eye