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pankajdubey wrote:ajatule sam?ne: why are these two word in masculine locative singular- does it deal with their respective positions in the group ?
No, that's actually the feminine nominative dual (because Aries and Libra are two signs and tul?, the final member of the compound, is feminine).

The text you've found (at DLI?) isn't a commentary but the actual text (m?lam?tra) of the H?yanaratna. As you can see, it shows that the rising times of Aries and Pisces are identical, and similarly of Virgo and Libra. It doesn't explain why Aries and Libra are called 'middling', 'equal' or 'similar', though.
https://astrology.martingansten.com/

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Martin Gansten wrote:
pankajdubey wrote:ajatule sam?ne: why are these two word in masculine locative singular- does it deal with their respective positions in the group ?
No, that's actually the feminine nominative dual (because Aries and Libra are two signs and tul?, the final member of the compound, is feminine).

The text you've found (at DLI?) isn't a commentary but the actual text (m?lam?tra) of the H?yanaratna. As you can see, it shows that the rising times of Aries and Pisces are identical, and similarly of Virgo and Libra. It doesn't explain why Aries and Libra are called 'middling', 'equal' or 'similar', though.
The DLI text end with iti followed by the explanation, so I thought it was a commentary on the original.

Pankaj

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A couple of observations about the ethics of the zodiac...

The upright signs approximate the solar half of the zodiac (Cap being the exception) and the lunar half the other side. The signs of the lights seem to be more "upright" than the signs of Saturn. This is only true in the northern hemisphere.

Mathematically it is possible for the signs adjacent Libra/Virgo (Leo/Scorpio) to have greater ascension than Libra/Virgo. I'm not sure how Scorpio can be considered more truthful (except for it being one of the mute signs) than Libra on the face of it, but in this world many things are upside down. Down under, however, the reverse.
Curtis Manwaring
Zoidiasoft Technologies, LLC

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I've been following this thread with interest, as I'm trying to get my head round the implications of rising times and their relationship to antiscia/contrantiscia. Pankadjubey clearly set out the relationships:
Capricorn 283
Aquarius 203
Pisces 158
--------------------
Aries 158
Taurus 203
Gemini 283

Cancer 363
Leo 395
Virgo 398
-------------
Libra 398
Scorpio 395
Sagittarius 363
Can anyone point me at a post or an article on the net to help me understand why the summer solstice > winter solstice signs should be longer and straighter, and the the winter > summer ones more oblique and shorter (in time)? i can't manage to visualise why the peaks of fast and slow rising (and of obliquity and straightness) should be at the equinoxes. I can see that this is true with an astronomy program, but can't work out why. We can also, I think, see things in terms of an acceleration from autumn equinox to spring and a deceleration from spring to autumn.

Also, if I understand right, there is a slight variation of rising times because of the precession (at a different rate than the VP) of the aphelion/perihelion axis, so the peak of rising times (and of straightness/obliquity?) will not in fact fall exactly on the equinoxes, but will vary slightly over time in a zodiacal direction, but this seems to be generally ignored in astrological discussions (e.g. Robert Hand's paper "On the Invariance of the Tropical Zodiac", and Deborah's "The Classical Basis of Antiscia". Presumably this shift would engender a slight difference even at the equator.

Many thanks for any help.
Graham

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Graham F wrote:Can anyone point me at a post or an article on the net to help me understand why the summer solstice > winter solstice signs should be longer and straighter, and the the winter > summer ones more oblique and shorter (in time)? i can't manage to visualise why the peaks of fast and slow rising (and of obliquity and straightness) should be at the equinoxes. I can see that this is true with an astronomy program, but can't work out why.
I can't point you to an article, but I can try to explain why this is, as I understand it in terms of observational astronomy.

Risings and settings are a function of the rotation of the celestial sphere, marked by the celestial equator, around the earth/point of observation. This rotation takes place at a constant speed, which is why we can express degrees of right ascension as time (15? = 1 hour).

Because of the different inclinations of the 12 signs (or, rather, the 6 pairs of tropical signs) to the equator, if we note the points on the equator rising with the beginning of each sign (for any given geographical latitude), the resulting 12 points will be spaced apart by different numbers of degrees. (Each such point will mark the oblique ascension of the beginning of a sign.) A sign located between two equatorial points 15? apart will rise in one hour; if they are 45? apart, it will take three hours. And the more 'upright' a sign is with regard to the local horizon, the further apart these points will be. So it's a function of (a) the angle between the horizon and equator and (b) the angle between the ecliptic and the equator.
Also, if I understand right, there is a slight variation of rising times because of the precession (at a different rate than the VP) of the aphelion/perihelion axis, so the peak of rising times (and of straightness/obliquity?) will not in fact fall exactly on the equinoxes, but will vary slightly over time in a zodiacal direction, but this seems to be generally ignored in astrological discussions (e.g. Robert Hand's paper "On the Invariance of the Tropical Zodiac", and Deborah's "The Classical Basis of Antiscia". Presumably this shift would engender a slight difference even at the equator.
I'm afraid this is beyond my ken as well.
https://astrology.martingansten.com/

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Capricorn 283
Aquarius 203
Pisces 158
--------------------
Aries 158
Taurus 203
Gemini 283

Cancer 363
Leo 395
Virgo 398
-------------
Libra 398
Scorpio 395
Sagittarius 363
I'm with Graham, in the sense that I can't understand why the rising times peak (high/low) in the equinoxs. Is there any mention on the text for which time of the year this table was calculated?

I think that the signs have different rising times during the year, as well as during the course of a single day as well. Or are those values obtained for when the sun is on those signs?


Jo?o Ventura

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Yes, I've been sitting here for the last few minutes wondering just that (why the high/low peaks are at the equinoxes). I can see that latitude and ecliptic obliquity would cause calculable variations, but I'd have thought the mean values would be at the equinoxes and the extreme ones at the solstices, but it's the reverse.
But unlike Joao, I think the rising times should be the same throughout the year at a given location, it's just that they will rise at different times of day or night. And each sign only rises once in a single day, so no variation there.
Graham

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The thing to think about is that the angle of the ecliptic with the equator is not perpindicular, or, more to the point, it isn't perpindicular to our latitude.

Think of a line drawn from the sun when it rises, when it culminates and when it sets. This line drawn through the sky is the diurnal arc which will be parallel to the equator. The ecliptic, however, does not run along this same diurnal arc you just drew in the sky. Instead, the ecliptic is going to be at an angle to this arc, the diurnal arc is parallel to the equator and we know the eclipitc is angled to the equator hence its angled to the diurnal arc too. I realise we all know this on paper but it's important to keep it in mind.

Here's an image which shows the position of the sun at varying points of the day. Running through each sun is a faint line which depicts where the ecliptic was at at that time of the day. As I say, we probably all know this, but it helps to see it.
Image
So when the earth rotates it's not rotating along the same line as the ecliptic.

Here's a short animation I just made to depict Aries and Libra as they rise. The thick red line can be imagined as an arc of 30 degrees of longitude which represents the tropical sign as it rises. Each frame of the animation elapses 15 minutes of clock time. Keep in mind that the earth rotates at a constant speed.

(I didn't embed these as the animation may get annoying)

Aries:
http://i.imgur.com/2soSh04.gif

Libra:
http://i.imgur.com/7crxzAz.gif

Notice that the rotation of the earth, as said above, is not along the same lines as the ecliptic, the rotation is not parallel to the ecliptic.

So here's what it looks like when I add in part of the diurnal arc in blue. It is along the blue line that we can imagine the earth to be spinning. So the longer the blue line the longer it will take the earth to allow a full sign to cross the horizon and rise.

Aries:
Image
Libra:
Image

Hopefully what should be obvious is that it's not so much the tilt of the ecliptic at the time that the sign is rising, it is the diurnal arc along which the ecliptic will rise at that time.

Clearly we see that Aries is much more slanted than Libra. And as a result, it is much shorter than Libra - the longer the line the longer it takes to rise as the earth rotates at a constant speed. Hence it takes Aries much quicker to rise than Libra, and also why we call Aries a crooked sign and Libra a straight one.

All these images were taken using Stellarium software, with me adding in the blue and red lines myself, and they were all taken at the latitude of London England. The further extreme the latitude, the more extreme will be the result.

Hope this helps.
"The only true wisdom is in knowing you know nothing" - Socrates

https://heavenlysphere.com/

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Paul wrote:So when the earth rotates it's not rotating along the same line as the ecliptic.
Yes, that's the main point. Thanks for the illustrations, Paul. Software is useful, but for those of us with poor visualization skills, I find an old-fashioned armillary sphere hard to beat. Just giving my desk-sized one a whirl as I write this, and watching the zodiac ring wobble -- most illuminating! :)
https://astrology.martingansten.com/

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Thanks for the reply Paul. I knew it had to do with the angle between the ecliptic and equator line, but my doubt was why it reached the max and min peaks on the equinoxes instead of the solstices.

So I downloaded Stellarium as well, and the "key" to the solution seems to be that the angle between the ecliptic and equator is maximum in the equinox, contrary to what I was visualizing..

I have to look at this a little bit better, still haven't made "the click"! :)

Edit: Ok, I got it now! Here's a sketch that I made to understand, maybe it can help someone as well! It's for someone at a northern latitude, and the lines of projection from ecliptic to equator mark the beginning and end of the sign.
Image

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Thanks to Paul for the great visuals
A nice video of an armillary sphere in operation, and the the diurnal path of the sun in the sky at spring equinox and the solstices:

https://www.youtube.com/watch?v=M0chCdFEaP0

Along with Paul's clips, this makes things clearer, though unforunately it doesn't show the autumn equinox solar path - this is what intrigues me, why is it the opposite of the spring one? The penny will drop, I'm sure, but I might need an armillary sphere...
Graham