astrologizing.net
DORIS HEBEL, a great Astrologer from Chicago, teaches this method for finding semi (45 degrees) and
sesqui (135 degrees) squares:

If the planet is lower than 15 degrees, add 15  to it and go up a quality.
If the planet is higher than 15 degrees, subtract 15 from it and go back a quality.

Qualities are three:  Cardinal, Fixed, Mutable.

The Moon is 4 degrees Fixed quality.  Add 15 to it and go up a quality to Mutable = 19 degrees.
Any planet at 19 degrees of Mutable quality is either 45 or 135 degrees from 4 degrees of Fixed Signs.

Mars is 19 degrees Mutable quality.  Subtract 15 from it and go back a quality to Fixed = 4 degrees.
Any planet at 4 degrees of a Fixed quality is either 45 or 135 degrees from 19 degrees of a Mutable Sign.

With practice, students will work with the minutes, also, to see if the aspect is applying or separating.
setstats
body.
When I started erecting birth charts, I used logarithms, then calculator, then computer. I'm still nasty at math, but here is a way to
figure out almost any aspect by hand.  The reason I brought this all back up in my memory is that I wanted to find my 5 pointed
quintile star that
ROBERT WILKINSON  talks about.

What you have to do is very simply use the 60 base, 30 base, and 12 base BECAUSE there are 60 minutes in a degree, 30
degrees in a Sign and 12 Signs in the Zodiac. Also, you have to remember how to borrow in these bases.  Got that?

For instance, if I want to find a quintile in my chart, I will use 72º to add to a planet. BUT, there are only 30º in any SIGN.  How
does 72º break down?  Well, we know that there are 30º in every Sign; there must be 2 Signs and 12º left over.  Let's do it.

1S  00º   00'  = 0º Aries     (72º = 2 Signs and 12º left over.  72º
+     72º          = Quintile                                                             -60 which equals 2 S or
(Signs)
-----------------                                                                            ----------------
3S  12º      or 12º Gemini 00'                                                    12º                    Gemini is Sign 3 out of 12.  Got it?)

Let's try something more difficult.  I have a t-quintile in my birthchart.  Mars quintiles Neptune and both biquintile Venus.  That
gives me the three points, but I want to fine the other 2 points to make Robert's Star Quintile.

I have Mars at 28º Scorpio 12' which equals  8S      28º       12'
                                                          +   2         12        00  (See where this came from?) It's a quintile!
                                                          ------------------------
                                                          10S     40º       12'  what's wrong with this figure?  There's only 30 degrees in a Sign.  So,
what do we do?                                                 -30
                                                           ------------------------
                                                           10       10         12  now what's wrong?  We took away 30, but where to put it?
                                                           +1
                                                           -------------------------
                                                            11S     10º      12'   which reads 10º Aquarius 12'   Yeah.....we did it!  No trig.

Now, let's find the other point in the Quintile star. This time may be a little harder. We'll subtract instead of adding.

My Neptune is 16º Virgo 12'         6s     16º      12'
Subtract a Quintile of 72º             - 2      12    
                                      ------------------------
                                        4s       4º       12'              The 5th point of the Quintile Star = 4º Cancer 12'.   To chart:
Some Great Things My Teachers Taught Me
The Kepler design has
specialized charts such as
this to show some minor
aspects all by themselves and
makes them easier to find.
However, one still has to
figure out the void points
which I have entered here.
Connect them to the other
three points and you have the
Quintile 5 pointed Star.

The letter, "A" means that the
aspect is applying. The letter,
"S" means that the aspect is
separating.
*10º [ 12'
* 4º r 12'
@
@
Ok, now I remember where I learned
this method; calculating the Arabic
parts.  Wow, that had to be at the very
beginning of my learning in the mid
60's. So, I probably got it from
Maryann Crabtree; ye gods, almost a
half century ago.
Today, Neptune and Pluto are only 1 minute off of a septile aspect.  Let's figure all the exact septile points
in the 7 pointed Star. We can start with Pluto:  
Pluto= 10s  00º  26'
Sep =+  1   21   26
-----------------
11s 21º  52' or
21º Aquar 52'

11s 21º  52'
+   1  21   26
-------------------------------
12   42   78
           -60  
----------------
12   43   18
    -30
------------------
13   13   18
-12
-------------------
1   13   18 or
13º Aries 18'  

1s  13º   18'
+  1    21    26  
-----------------
2    34    44
   - 30
-------------------
3s      4º   44' or
4º Gemini 44'

3s      4º    44'
1      21    26
----------------------
4      25    70
     +  1   -60
------------------------------
4s    26º  10'  or
26º Cancer 10'

4s   26º   10'
 1    21     26
-------------------
 5    47     34
+1   -30
--------------------------------
 6s  17º     34' or
17º Virgo 36'

  
6s 17º   34'
+  1   21    26
--------------------
  7    38    60
                -60
--------------------
7s    39º   00'
    - 30
-------------------------------
9º Scorpio 02'

8s     9º   00'
+  1    21   26
----------------------
10s   00º  26' or
00º Capricorn 26'
Now, wasn't that fun??? That's why it took us
dinosaur astrologers so long to compute charts
back in the 60's.

Actually, I miss it.  While I was fooling with the
math and computations and entering everything
by hand around the chart wheel, I was getting into
the person bit by bit.  By the time I was finished, I
felt like I really knew the person and it was good.  

When I get a chart in 2 seconds from the
computer, it's a cold piece of paper and has none
of me in it, nor the person in me. Why don't I just
go back to doing charts by hand?  Because then I
would have to charge a fee.  Even though I'm
retired, my time is still precious, if only to me.