It looks like it is paralleling the earlier phrase of "you have placed":

when you have placed your eye exactly on the edge of the table, the penny will then have ceased to appear oval...

If you wanted to use "will cease," a more elegant form of the sentence would use "place" instead of "have placed":

when you place your eye exactly on the edge of the table, the penny will then cease to appear oval...

In the first version, both use the future perfect tense, as opposed to the use of the present tense for a future event. Both options are fine, but you can't mix the two.

It looks like it is paralleling the earlier phrase of "you have placed":

when you have placed your eye exactly on the edge of the table, the penny will then have ceased to appear oval...

If you wanted to use "will cease," a more elegant form of the sentence would use "place" instead of "have placed":

when you place your eye exactly on the edge of the table, the penny will then cease to appear oval...

In the first version, both use the future perfect tense, as opposed to the use of the present tense for a future event. Both options are fine, but you can't mix the two. The reason for using the future perfect is that of the author, and deals with the context of the sentence in the book.

It looks like it is paralleling the earlier phrase of "you have placed":

when you have placed your eye exactly on the edge of the table, the penny will then have ceased to appear oval...

If you wanted to use "will cease," a more elegant form of the sentence would use "place" instead of "have placed":

when you place your eye exactly on the edge of the table, the penny will then cease to appear oval...

In the first version, both use the future perfect tense, as opposed to the use of the present tense for a future event.

It looks like it is paralleling the earlier phrase of "you have placed":

when you have placed your eye exactly on the edge of the table, the penny will then have ceased to appear oval...

If you wanted to use "will cease," a more elegant form of the sentence would use "place" instead of "have placed":

when you place your eye exactly on the edge of the table, the penny will then cease to appear oval...

In the first version, both use the future perfect tense, as opposed to the use of the present tense for a future event. Both options are fine, but you can't mix the two.