Ah, well how stupid am I. I forgot to explain the whole premise behind the two theories.
Okay, this Egyptian Method Ptolemy relates is Angle/Pivot-based.
If the Hyleg is found in Quadrant II -- a Feminine Quadrant comprising the 7th, 8th and 9th Houses --- then the Hyleg and any Planets in the 7th, 8th or 9th Houses, are directed to the Descendant Point. The Arc of Direction is the "base years" and the Arcs for Benefics/Malefics in Quadrant II add/subtract to that.
If the Hyleg is in Quadrant I -- a Masculine Quadrant of the 12th, 11th and 10th Houses, then, uh, well, here's where Zoller and a few others are going to have a cow.
Most say to direct the Hyleg and Planets to the MC. That isn't exactly what Ptolemy says; they confused the technique of directing with the technique for determining life span; that would be really hard to do since they didn't use the MC for a long time; and even when they were using the MC, it was actually the 0° Point of the 10th Sign.
You actually direct the Ascending Degree in Primary Motion (clock-wise) to the Planets in Quadrant I.
Anyway, there are like some 50+ surviving manuscripts of Ptolemy's work, and no, Ptolemy did not write them, rather other people copied them from other manuscripts, including the original manuscript. All manuscripts have variations and deviations from one extent to another, including the chapters being arranged out of order and amendations and deletions to the text.
So, now we can see how doctrines and concepts get messed up in translation and misunderstanding over the centuries (and even recent days apparently).
As I mentioned on another thread, Ptolemy retells a method of calculating a Conception Chart, and from this Conception Chart, Ptolemy claimed one could determine the Native's future rank or station in life, whether the birth would be a single birth, or a multiple birth (like twins) and whether the child would be born deformed or have birth defects.
Someone copying Ptolemy's manuscript re-arranged the order of the chapters to make it appear that Ptolemy was using the Natal Chart to determine the Native's rank and station in life....instead of the Conception Chart.
Fast forward a few centuries, and you have Jewish and Arab astrologers pulling out their hair....or maybe their beards...trying to figure out why they keep failing when using Ptolemy's...on a Natal Chart....because they don't understand that Ptolemy was using a Conception Chart.
So they try to crow-bar a new scheme of "body-guarding" to conform with Ptolemy's method.
That fails...obviously...so a few centuries later, they try to crow-bar a second scheme of "body-guarding" into the Natal Chart.
That failed, too.
So here we all are.....centuries later.....still trying to figure out how to determine a person's rank and fame in life.
That same sad story repeats itself with the Hyleg.
From 1900 BCE to 1700 CE, the Human Race actually got really dumb before they started to get smart (or I suppose less dumb), and they still ain't really all that.
Armed with really bad copies of Ptolemy's work containing amendations, errors and omissions, and not knowing a thing about math and how to calculate ascensional differences and things, the Latins, Jews and Arabs are trying to figure out Ptolemy's scheme of longevity predicting....they can't do it....maybe they're looking for short-cuts.....so they crow-bar another technique on top of Ptolemy's Egyptian Method, and that's how we end up with the Hyleg & Alcochoden.
Like Math and Science, in Astrology, you can get the right result for the wrong reasons.
Their work-around for the Egyptian Method of longevity prediction works....for awhile, and then it breaks down, and when it does....that's when people start creating "exceptions to the rules"....now you can have the Sun in the 8th and the Moon Below Earth in the 3rd House and blah, blah, blah, blah....except that each new "exception to the rule" only creates more exceptions, because the method keeps breaking down.
So here we all are.....centuries later.....still trying to figure out how to determine a person's longevity.
The Hyleg & Alcochoden Method is very arbitrary and highly subjective, which is why it sometimes gives the correct answer, and sometimes not.
The Hyleg Method with Primary Directions is based on math and science, is much less subjective, and consistently yields more accurate results.