The key insight was to replace the law of cosines by a law of versed sines or a law of suversed sines, where the suversed sine of an angle is the versed sine of the supplement of that angle.

a yellow satin train that streeled after her like the tail of a comet

I mean to have them all garrisoned again within the year, and nightfires burning before their gates.

The spade foot leg may be used as an alternate design.