Ibn Ezra as Placidus’s preincarnation

I think every astrologer knows that there is a Placidean house system. Some of astrologers are informed that Placidus is not the inventor of this house system. Few astrologers heard that Avraham Ibn Ezra wrote about this system five centuries before Placidus. But much less number of astrologers know what and where Ibn Ezra really wrote.

Ibn Ezra really described the house system that is based on the hour distance of the point of ecliptic from the meridian. And it is really the same basic idea as in Placidean house system.

Ibn Ezra describes this system in his ספר הטעמים א (The Book of Reasons A). A is important in this case, because there are two versions of The Book of Reasons – version A and version B. Version A is more than twice bigger than version B. But the English translation of The Book of Reasons by Meira Epstein is based on the version B. Therefore English speaking readers are bereft of some very interesting and important parts of this Ibn Ezra’s work, including the part on house system.

I place here this part for those who can read Hebrew.

I don’t give a complete translation of this fragment, only beginning that is useful for my purpose. And my purpose is to show how Ibn Ezra finds those points of the ecliptic, i.e. to unscramble his way of calculations.

Ibn Ezra was very versed in mathematics and astronomy, but he didn’t have  Napier’s formulas etc., of course. Nevertheless, he resolved the problem with the tools he had and with tedious iterative method.

Ibn Ezra says (many thanx to Danny Steinhoff for his translation, by the way :

And now I give you the way of equation of four houses. Look how many right degrees are between the ascending degree and the Line of the Abyss. Take one third of them, and add it to the ascending degree calculated in right degrees. Find a value of a temporal hour that corresponds to the degree obtained in result of the addition in a table of the region. Double the hours and minutes, and add the result to the equatorial degrees corresponding to the ascending degree. If the sum is equal to the degree calculated before, this is the beginning of the second house. If the result of the addition is greater than calculated degree, then subtract one or two degrees. And find to what temporal hour corresponds the degree obtained after the subtraction. And do so untill you find the degree and minute, which are the beginning of the house. But if the sum is less, do the contrary, i.e. add a degree. And then do the same as said before.

First, we must clarify Ibn Ezra’s terminology.

A temporal hour is a temporal hour. Ibn Ezra mentions it in hours and minutes, because temporal hours were presented in medieval tables in this form. But now we rather express them in degrees.

Right degrees are just the degrees of the ecliptic. Ibn Ezra describes the equal house system as well. As he says, the equation in all climes according to right zodiacal degrees (מעלות גלגל המזלות שהם ישרות)… The rule is: give 30 degrees to every house, beginning from the ascending degree.
This מעלות גלגל המזלות שהם ישרות (right Zodiacal degrees) are obviously the degrees of the ecliptic. Therefore Ibn Ezra’s מעלות ישרות are the same as gradus aequales (the equal degrees) in medieval Latin texts.

The right degrees between the ascending degree and the Line of the Abyss are degrees of ecliptic between Ascendant and Imum Coeli.

The equatorial degrees corresponding to the ascending degree is the oblique ascension of the Ascendant.

Now we can proceed to the testing of Ibn Ezra’s method.
Let’s take a chart for testing:
February, 7th, 2009
11h00min (GMT +3)
Nizhny Novgorod, Russia
56n20 44e00

MC is 29°25′ of Capricorn
Ascendant is 10°36′ of Gemini
IC is 29°25′ of Cancer

We can find the right ascension of MC anf the oblique ascension of the Ascendant with Ascensions And Descensions Calculator.
Year: 2009
Pole: 56°20′ (i.e. the geographical lattitude of the chart)
Ecliptical latitude is 0, because we work with the points of the ecliptic.

Ecliptical longitute of MC is 299°25′.
And we get the right ascension 301°34′.

Ecliptical longitude of the Ascendant is 70°36′.
And its oblique ascension is 31°35′.

1. We must find the distance between the Ascendant and IC in degrees of the ecliptic.
119°25 – 70°36′ = 48°49′

2. We must find one third of this, i.e. divide it by three.
48°49′ / 3 = 16°16′

3. We must add it to the Ascendant (in degrees of the ecliptic).
70°36′ + 16°16′ = 86°52′

4. Now we must find the right ascension and declination of this point of the ecliptic. We can use The Convertor Of Coordinates for it.
Year: 2009
Ecliptical longitude: 86°52′
Ecliptical latitude: 0
And we get the right ascension: 86°35′
Declination: 23n24

5. Now we must find the nocturnal temporal hour of this point. We can use Hour Distance Calculator for this purpose.
Geographical lattitude: 56°20′
Right ascension of MC: 301°34′
The point is below the horizon
Right ascension: 86°35′
Declination: 23°24′
And we get the nocturnal temporal hour: 8.2471°

6. Multiply it by two, because every house is equal to two temporal hours.
8.2471° x 2 = 16.4942
Or 16°30′.

7. We add it to the oblique ascension of the Ascendant.
31°35′ + 16°30′ = 48°05′

8. This oblique ascension corresponds to 88°47′ of the ecliptic.

9. 86°52′ is less than 88°47′. Therefore we add 1°.
86°52′ + 1° = 87°52′
And repeat the cycle beginning from the item 4.

We find right ascension and declination.
Right ascension: 87°41′
Declination: 23n25

We find the nocturnal temporal hour: 8.2405°.

We multiply it by two: 8.2405° x 2 = 16,481 or 16°29′.

We add it to the oblique ascension of the Ascendant:
31°35′ + 16°29′ = 48°04′

It corresponds to 88°46′ of the ecliptic.

10. 87°52′ is still less than 88°46′. But the difference is less than 1°, therefore let’s add 30′.
87°52′ + 30′ = 88°22′
And repeat the cycle again.

We find right ascension and declination.
Right ascension: 88°13′
Declination: 23n26

We find the nocturnal temporal hour: 8.234°.

We multiply it by two: 8.234° x 2 = 16,468 or 16°28′.

We add it to the oblique ascension of the Ascendant:
31°35′ + 16°28′ = 48°03′

It corresponds to 88°45′ of the ecliptic.

11. 88°22 is still less than 88°45′, therefore we must add again…

You can continue this captivating pursuit, if you want

Theoretically, we must get the equation when we come to the cusp of the Placidean second house.
Modern calculation gives the cusp 28°45′ of Gemini, i.e. 88°45′. Let’s check, is there the equation or not.

We find right ascension and declination.
Right ascension: 88°38′
Declination: 23n26

We find the nocturnal temporal hour: 8.234°.

We multiply it by two: 8.234° x 2 = 16,468 or 16°28′.

We add it to the oblique ascension of the Ascendant:
31°35′ + 16°28′ = 48°03′

It corresponds to 88°45′ of the ecliptic.
88°45′ is equal 88°45′
Bingo!

Well, now we know exactly that Avraham Ibn Ezra really described the house system in one of his book, and that his way of calculations really works. But is it the house system known today as Placidus house system?
From one hand, the points of the ecliptic calculated with Ibn Ezra’s algorithm are the same as calculated according to Placidus (or Girolamo Diedo). And the base of the system (every house is equal to two temporal hours) is the same. But Ibn Ezra gives only calculations for the points of the ecliptic, and what about other points of the celestial sphere?
In other words, this glass is half full or half empty. Anyway, it is your glass

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