Starting with your cylinders around arbitrary minor axes, your work here is by and large coming along quite well. You're drawing your linework with a great deal of confidence, which helps to achieve smoother and more evenly shaped ellipses, while also keeping your lines straighter. I'm also pleased to see that as you check your minor axis lines after the fact, you are picking up on fairly small discrepancies, which is important as it helps you to continue to improve your estimation of those alignments, rather than plateauing when as you get into the "close enough" territory.

I am also pleased to see that you approached a good variety of rates of foreshortening across the set, although I did notice one thing that I wanted to explain - although this isn't a mistake, in the sense that I don't mention it in the lesson material. I find that giving students the room to potentially figure this out themselves helps the concept to stick more strongly. To be completely honest, I generally felt that you did grasp this concept on some level already.

So, what is that concept? Well, it's the fact that both the shift in scale (where due to the convergence of the side edges of our cylinder, the far ellipse ends up smaller overall than the end closer to the viewer) and the shift in degree (where the far end is wider), are both manifestations of foreshortening, and so it is necessary for both of them to operate in tandem with one another. To put it simply, this means that if the side edges are converging more rapidly, resulting in the far end being noticeably smaller, the far end also needs to be noticeably wider. The viewer will notice that something looks "off" in cases like 127 on this page, where that far end really should be wider to match the shift in scale.

Continuing onto the cylinders in boxes, you've similarly done quite well here. This exercise is really all about helping develop students' understanding of how to construct boxes which feature two opposite faces which are proportionally square, regardless of how the form is oriented in space. We do this not by memorizing every possible configuration, but rather by continuing to develop your subconscious understanding of space through repetition, and through analysis (by way of the line extensions).

Where the box challenge's line extensions helped to develop a stronger sense of how to achieve more consistent convergences in our lines, here we add three more lines for each ellipse: the minor axis, and the two contact point lines. In checking how far off these are from converging towards the box's own vanishing points, we can see how far off we were from having the ellipse represent a circle in 3D space, and in turn how far off we were from having the plane that encloses it from representing a square.

In applying the line extensions as carefully and mindfully as you have here, you've been giving yourself a solid analysis of the work from each page, being able to identify where you could adjust your approach to help bring those convergences in and make them more consistent for the next page, and I can see your sense of those proportions improving over the course of the challenge. At this point, you should be well equipped for what the next lesson will ask of you, and while there is always room for continued growth in this area (which is why it becomes part of our warmups, like all the other exercises), you're where you ought to be.

So! I'll go ahead and mark this challenge as complete. Keep up the great work.