De Morgan's categorical types

In a comment to the last post, Brandon asked what would be the equivalent of De Morgan's "zodiac" (section 48 of the "Syllabus of a Proposed System of Logic") in my notation?

Here it goes:
1. Let's enumerate symbols in zodiac with clock numerals, so that 12 is in the top, 3 on right, 6 in bottom, 9 on left.
1 )( 2 () 3 )) 4 ).) 5 ).) 6 ).( 7 () 8 )( 9 (.) 10 ).) 11 ).) 12 ))

Corresponding formulas in my notation (for coherence I'll use De Morgan's letters):
A. Read clockwise
1 (-X-Y) 2 (+X+Y) 3 [-X+Y] 4 (-X+Y) 5 (-X+Y) 6 [-X-Y]
7 (+X+Y) 8 (-X-Y) 9 [+X+Y] 10 (-X+Y) 11 (-X+Y) 12 [-X+Y]

B. Read counterclockwise (ie. assymmetric formulas change)
1 (-X-Y) 2 (+X+Y) 3 [+X-Y] 4 (+X-Y) 5 (+X-Y) 6 [-X-Y]
7 (+X+Y) 8 (-X-Y) 9 [+X+Y] 10 (+X-Y) 11 (+X-Y) 12 [+X-Y]

Universal syllogisms are composed of universal premises at 12, 3, 6 and 9, read either clockwise or counterclockwise:

a1) 12[-X+Y]+3[-Y+Z]=[-X+Z]
a2) 3[+Z-Y]+12[+Y-X]=[+Z-X]
b1) 3[-X+Y]+6[-Y-Z]=[-X-Z]
b2) 6[-Z-Y]+3[+Y-X]=[-Z-X]
c1) 6[-X-Y]+9[+Y+Z]=[-X+Z]
c2) 9[+Z+Y]+6[-Y-X]=[+Z-X]
d1) 9[+X+Y]+12[-Y+Z]=[+X+Z]
d2) 12[+Z-Y]+9[+Y+X]=[+Z+X]

For every universal syllogism there are two opposed syllogisms, constructed of one universal premise retained from universal syllogism and of a particular premise adjacent to it in zodiac but "external", which is contradictory to the conclusion of the corresponding universal syllogism. Premises are read in opposite direction to the universal syllogism they oppose, and retained universal premise is converted. I understand that adjacent "external" formulas in comparison to eg. 12 and 3 are correspondingly 11 and 4. Hence:

a11) 12[+Y-X]+11(+X-Z)=(+Y-Z)
a12) 4(+X-Z)+3[+Z-Y]=(+X-Y)
a21) 3[-Y+Z]+4(-Z+X)=(-Y+X)
a22) 11(-Z+X)+12[-X+Y]=(-Z+Y)
b11) 3[+Y-X]+2(+X+Z)=(+Y+Z)
b12) 7(+X+Z)+6[-Z-Y]=(+X-Y)
b21) 6[-Y-Z]+7(+Z+X)=(-Y+X)
b22) 2(+Z+X)+3[-X+Y]=(+Z+Y)
c11) 6[-Y-X]+5(+X-Z)=(-Y-Z)
c12) 10(+X-Z)+9[+Z+Y]=(+X+Y)
c21) 9[+Y+Z]+10(-Z+X)=(+Y+X)
c22) 5(-Z+X)+6[-X-Y]=(-Z-Y)
d11) 9[+Y+X]+8(-X-Z)=(+Y-Z)
d12) 1(-X-Z)+12[+Z-Y]=(-X-Y)
d21) 12[-Y+Z]+1(-Z-X)=(-Y-X)
d22) 8(-Z-X)+9[+X+Y]=(-Z+Y)

Wow! That was not easy but it works. Was that a memory-device?