Starting at the Eastern horizon (far left) we have Aries
whose glyph is shaped like the horns of a ram.  
Moving downward, lies Taurus with the bull's horns,
then the Twins, Gemini.  At the bottom is Cancer and
then comes Leo with his curling tail.  The Virgin,
Virgo with her legs crossed is next and then the
balanced Sign, Libra, opposite of Aries.

The eighth Sign is Scorpio, the M with the pointed tail
(just the opposite of Virgo, the M with her legs
crossed).  You can read the story about the
Sagittarius comes after Scorpio with his arrow
aiming as high as his ideals.  Capricorn the goat is
next and the highest point of the chart (ahem), then
the air waves of Aquarius. Finally, the Sign of the fish,
Pisces, however the fish are tied together trying to
each go his own way.  Sounds a bit like our political
system, no?
Thoughts on Semisquares & Sesquiquadrates
J. Sue Gagliardi
Thoughts on Semisquares and Sesquiquadrates (Sesquares for short)

We talk about the opposition (180º) as if it were a force of differences.  However, in the elements of Fire,
Earth, Air, and Water, the elements of the opposition are compatible and balanceable.  Half of the
opposition, the square (90º), is made up of incompatible elements; fire to earth and water, earth to fire and
air, air to earth and water, and water to fire and air.  These aspects are easy to see in a chart.  

However, halve the square to 45º and and the semisquare is not so easy to see at first glance.  
Semisquare are made up by Signs that are right next to each other and the elements come to the fore
again;  Aries fire to Taurus earth = incompatible.  Taurus earth to Gemini air =  incompatible; all the way
around to Pisces water to Aries fire = incompatible. So, semisquares are made up of half incompatible
Signs and, though they do not force action as do the squares, they stick in the craw and create inflamation
that is hard to eliminate. The ones that form compatible elements are not so difficult. See below:

Years ago, Doris Hebal taught how to figure semi and sesqui squares.  If the planet is under 15º, add 15
to it and go up a quality (cardinal, fixed, or mutable).  If the planet is over 15º, subtract 15 from it and go
back a quality.  Let's see how that works:
Ever aware that there are 12 Signs, 30 degrees to each Sign and 360º to a wheel, we start our figuring:
Pretend that each Sign begins at 2º and we want to find the semisquare 45º and sesquares 135º around
the wheel from 2º.

Start at 2º Aries on the far left.  Where would the semisquares fall?

Ad 15 to 2º and you get 17º of the next quality.  What is it?  Since Aries is Cardinal, it must be Fixed, yes?
Yes, it is fixed.  Where are the nearest fixed Signs?  Note the red stars at 17º of Taurus and Aquarius;
those are the semisquares; one compatible (Aquarius) and one incompatible (Taurus).  Fire and Air are
compatible and Fire and Earth are not.

What about sesquares (sesquiquadrates) at 135º?  They follow the same rule and follow the opposite of
the semisquares.  See the blue stars in Leo and Aquarius.  They are 135º from 2º of Aries.

If semiquares are half of a square, the sesquare is a square and a half 90 + 45.  This makes the sesquare
more difficult than the semisquare, more anxiety prone.  It's like, "I've already been here and done this; why
am I here again?" You simply have to be tested one more time just to see if you have it conquered;
whatever "it" is.  Too, the sesquare is different from the other major aspects in that it is not divisible by an
even number 360/135 = 2.666.  Does something about that number speak to you???