Overall you've done really well, there are just a few things I want to draw to your attention.

With the first section - the cylinders around arbitrary minor axes - you've done a great job of exploring and experimenting with a wide variety of rates of foreshortening. You've got some with shallow foreshortening, some with more dramatic foreshortening - and some, i noticed, appear to have no foreshortening at all.

This last group - for example, cylinder 150 where the side edges appear to be parallel, converging towards a vanishing point "at infinity" (as discussed way back in Lesson 1) are technically incorrect. This is because a vanishing point will only go to infinity, resulting in lines that are parallel on the page, when the lines it governs run perpendicular to the viewer's angle of sight (which would be the same as running parallel to the picture plane, so across the viewer's field of view, not tilting towards or away from them at all).

In any other orientation (150 doesn't appear to be parallel to the picture plane, since the ellipses on either end suggest that they're turned partially away from the viewer), a lack of foreshortening like this tells the viewer that there is zero distance between the ends of the form - something that we can see just by looking at the drawing is incorrect. This means we end up with a contradiction in the drawing - certain signs point to the cylinder having at least the length we can see on the page, and other signs suggest that it has no length at all. The viewer will pick up on these kinds of things, noticing that the cylinder looks "off" even if they can't put their finger on why.

Now this isn't an issue that came up often at all, but it does also relate to another issue that came up once or twice in your set. Again - not common, but still worth calling out. When it comes to foreshortening, there are two major ways in which it is represented in a drawing. One is the shift in scale from one end to the other (the result of the convergence of those side edges), and another is the shift in degree (where the far end is wider than the closer end). Both of these tell the viewer whether the cylinder is basically as long as we can see on the page, or whether there is additional length that is "unseen" (existing in the dimension of depth, which cannot be captured directly on the flat page).

If you look at an example like number 48, we can see a case where the shift in scale is pretty significant, but the shift in degree is quite minimal. 52 is quite similar as well. In this case, one of these shifts suggests a more significant foreshortening, and the other suggests minimal foreshortening - again, a contradiction. Since they both represent the same thing, these two shifts should be generally similar - both dramatic, or both shallow.

But again - these issues were quite uncommon in your set, and only came up a few times. I just wanted to make sure you understood the concept.

Continuing onto your cylinders in boxes, these are really well done. This exercise focuses on training students to figure out how to construct boxes that specifically feature a pair of opposite faces which are proportionally square. We do this by taking the line extensions from the box challenge (which help us establish whether or not the box's lines converge towards consistent vanishing points), and add to it the ellipses and their own lines (the minor axis and contact point lines). When the ellipses' lines align with the box's vanishing points, we know that the ellipses themselves represent circles in 3D space - and therefore the plane enclosing it would represent a circle in 3D space. If we're off by somewhat, we can make adjustments in our next page to bring them a little closer, further training our brain to identify the relationship between how the box is drawn on the page, with its own foreshortening and other elements, and how that can impact the proportion that is drawn.

These are all things that happen subconsciously - our brains are remarkable things, and even if we're not trying to attack a certain problem directly, this kind of thing can train us to develop an intuition for what kind of proportions may be more or less correct. In this regard, you've done a great job, and the fastidiousness with which you've extended and studied your line extensions has made a considerable difference.

All in all, very nice work. I'll go ahead and mark this challenge as complete.