Starting with your cylinders around arbitrary minor axes, there's a lot here that's coming along well:

• Your linework is smooth and confident - you're clearly making good use of the planning/preparation techniques we've explored throughout this course to ensure evenly shaped ellipses and greater precision with your lines.

• You're fastidious and patient in the analysis of your true minor axes, identifying even fairly small deviations so as to continue improving and learning from those mistakes.

• You're doing a good job of incorporating a variety of rates of foreshortening

There are also one main thing that could be improved upon:

• One of the reasons I specifically ask for more variety in the rates of foreshortening is that when students explore more dramatic foreshortening, it can reveal certain small misunderstandings. One such misunderstanding can be seen in some of your cylinders, for example this one on the page marked '146' (though there are plenty of others spread out across your work. The issue comes down to this - in our cylinders, there are two main changes between the ellipse on the closer end and the ellipse on the farther end. One is a shift in overall scale, where due to the convergence of the side edges the far end gets notably smaller. The other is a shift in degree where the far end gets wider than the end closer to the viewer. While you do appear to understand both of these just fine, what we're missing in this cylinder and the others like it is that those two "shifts "need to occur at a similar rate - either both remaining fairly gradual/shallow, or both occurring in a more dramatic, exaggerated fashion. Here we get an exaggerated shift in scale, suggesting lots of foreshortening and that a good chunk of the cylinder's length exists in the unseen dimension of depth - and a gradual, minimal shift in degree that suggests the opposite. While the viewer won't be able to identify exactly what the issue is, they will be able to tell that something feels off.

Aside from that, your work throughout this part of the challenge is coming along well.

Moving onto your cylinders in boxes, 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 regards to the use of the line extensions/analysis to help push your boxes towards the correct proportion, you've done well. I do think that there's still plenty of benefit to continuing to focus your practice on the core 6 edges of the boxes themselves however, especially when your boxes get a little longer in one dimension. For example, as we can see on this cylinder, when the form gets longer you tend to have the blue and purple lines converging in pairs.

This does improve however, and the severity of these issues decrease as you get towards the end of this set. Still, keep working to refine your estimation of those convergences and you should continue to see considerable growth - simply because it's such a core concept to the principles of perspective.

Anyway, all in all you're progressing well. I'll go ahead and mark this challenge as complete.