# What's the meaning of “at least as important are …” in the following sentence?

Changes in the geometric properties of the joint with wear occur slowly for a lower pair. At least as important are the simple geometries of the relative motions that these joints permit.

I don't understand the last sentence.

• "At least as important" points out that the relative motions that the joints permit are, at minimum, equally important or more important than the changes in the geometric properties. – Sid Mar 15 '17 at 6:48
• For future reference, please include more details, like where you found this and what you think it means. This will help keep your question open. See Details, Please. – Em. Mar 15 '17 at 6:52
• Changes in the geometric properties of the joint with wear occur slowly for a lower pair. Just as important are the simple geometries of the relative motions that these joints permit. Of the same importance are the simple geometries of the relative motions that these joints permit. Note that, for me, personally, I would also infer, "Just as important, if not, more important, are the simple geometries of the relative motions that these joints permit. – Teacher KSHuang Mar 15 '17 at 9:47

In that sentence, "at least as important as" compares:

• changes (in the geometric properties...)

with

• (simple) geometries.

The meaning is that the geometries:

• have the same importance as the changes;

or:

• have more importance than the changes;

but not:

• have less importance than the changes.

From the Cambridge Dictionary

at least = as much as, or more than, a number or amount:

• It will cost at least \$100.
• It will be £200 at the very least.
• You'll have to wait at least an hour.

and:

Also from Cambridge Dictionary

As … as = We use as + adjective/adverb + as to make comparisons when the things we are comparing are equal in some way:

• The world’s biggest bull is as big as a small elephant.
• The weather this summer is as bad as last year. It hasn’t stopped raining for weeks.
• You have to unwrap it as carefully as you can. It’s quite fragile.