Brihat Parashara Hora Shastra · Volume 2
69. TRIKONA SHODHANA (REDUCTIONS) IN ASHTAKAVARGA SYSTEM
एवं सलग्नखेटानां विधायाष्टकवर्गकम् ।
त्रिकोणशोधनं कुर्यादादौ सर्वेषु राशिषु ॥ १ ॥
त्रिकोणं कथ्यते विप्र ! मेष-सिंह- धनूंष्यथ ।
वृष- कन्या - मृगास्याश्च युग्म तौलि घटास्तथा ॥ २ ॥
कर्क- वृश्चिक- मीनाश्च त्रिकोणाः स्युः परस्परम् ।
1-2 : Maharishi Parasara said - O Vipra ! After making ready the format of the Ashtakavarga of all the planets alongwith the Ascendant, in the described manner (in the foregoing Adhyaya), Trikona shodhana (Triangular Reduction) has to be carried out for all the signs. Three signs mutually located at an equidistant are known as Trikona Rashi (Triangular signs). For example, Aries, Leo and Sagittarius; Taurus, Virgo, Capricon; Gemini, Libra, Aquarius and Cancer, Scorpio, Pisces are the triads of the Trikona signs.
अधोऽधः सर्वराशीनामष्टवर्गफलं न्यसेत् ॥ ३ ॥
त्रिकोणेषु च न्न्यूनं तत्तुल्यं त्रिषु शोधयेत् ।
एकस्मिन् भवने शून्यं तत् त्रिकोणं न शोधयेत् ॥ ४ ॥
समत्वे सर्वगेहेषु सर्वं संशोधयेद् बुधः ।
पश्चात् विपश्चिता कार्यमेकाधिपतिशोधनम् ॥ ५ ॥
3-5 : The number of Rekhas obtained in the Ashtakavarga of the planets, the Sun, the Moon etc., be written below the signs of Aries, Taurus etc. Amongst the triad of Trikona signs, whichever sign has lesser number of Rekhas, the same number be deducted from the number of Rekhas of all the three signs and the remainder be written under each of them. In the Trikona signs, if any sign is devoid of any Rekha, no Shodhana would be necessary. If all the three signs are having equal number of Rekhas, the Shodhana of all the three signs should be carried out. This should be followed by the Ekadhipatya Shodhana (Reductions).
Example: 93
Data : Date of birth 6-9-1977; Time of birth 21-30 hrs. (IST); Latitude 28°-43' N; Longitude 77°-47' E.

Suppose we are to cast the Ashtakavarga Chart for the Sun, we need to locate the Rekhaprada (auspicious positions) and Binduprada (inauspicious positions) with respect to the radical position of the Sun. Let us first recapitulate the principles expounded in the previous chapter and list out these positions for the ready reference of the readers. These are as follows:
Sun's Ashtakavarga : Rekhaprada auspicious positions
| From the | : | Number of Positions |
| Sun | : 1st, 2nd, 4th, 7th, 8th, 9th, 10th, 11th | 8 |
| Moon | : 3rd, 6th, 10th, 11th | 4 |
| Mars | : 1st, 2nd, 4th, 7th, 8th, 9th, 10th, 11th | 8 |
| Mercury | : 3rd, 5th, 6th, 9th, 10th, 11th, 12th | 7 |
| Jupiter | : 5th, 6th, 9th, 11th | 4 |
| Venus | : 6th, 7th, 12th | 3 |
| Saturn | : 1st, 2nd, 4th, 7th, 8th, 9th, 10th, 11th | 8 |
| Ascendant | : 3rd, 4th, 6th, 10th, 11th, 12th | 6 |
| Total auspicious positions | 48 |
The rest of the places will denote the Binduprada (inauspicious positions) in the Sun's Ashtakavarga, which will be as follows:
Binduprada inauspicious position :
| From the | : | Number of Positions |
| Sun | : 3rd, 5th, 6th, 12th | 4 |
| Moon | : 1st, 2nd, 4th, 5th, 7th, 8th, 9th, 12th | 8 |
| Mars | : 3rd, 5th, 6th, 12th | 4 |
| Mercury | : 1st, 2nd, 4th, 7th, 8th | 5 |
| Jupiter | : 1st, 2nd, 3rd, 4th, 7th, 8th, 10th, 12th | 8 |
| Venus | : 1st, 2nd, 3rd, 4th, 5th, 8th, 9th, 10th, 11th | 9 |
| Saturn | : 3rd, 5th, 6th, 12th | 4 |
| Ascendant | : 1st, 2nd, 5th, 7th, 8th, 9th | 6 |
| Total auspicious positions | 48 |
By inplanting the Rekhas and Bindus (small verticle lines and dots), an Ashtakavarga for the Sun could be charted out. Let us once again revert to the model example and work out the Ashtakavarga for the Sun :
In the model horoscope, the Sun is located in the 5th position from the Ascendant (5th house in the Leo sign). Therefore, the auspicious positions (benefic places) there from (Leo sign be taken as 1st position) will be 1st (Leo) 2nd (Virgo), 4th Scorpio, 7th Aquarrius, 8th Pisces, 9th (Aries), 10th (Taurus), 11th Gemini - totally 8 benefic posited (Rekha prada). The rest of the places will be malefic places (Binduprada).
Sun's Ashtakavarga from the Sun :

Similarly the Sun's Ashtakavarga from the Moon could be drawn, after applying benefic and malefic positions as indicated previously.

Sun's Ashtakavarga from Mars:

Sun's Ashtakavarga from Mercury:

Sun's Ashtakavarga from Jupiter

Sun's Ashtakavarga from Venus

Sun's Ashtakavarga from Saturn

Sun's Ashtakavarga from Ascendant

Now all the 8 charts pertaining to the Ashtakavarga of the Sun can be reduced to a single chart clubbing togather all the Rekhas and Bindus (Benefic and malefic places) which will be the Ashtakavarga of the Sun showing the contributions both Rekha and Bindus from all the planet including the Ascendant. The format of the Sun's Ashtakavarga will be as follows:

After completing the Ashtakavarga of a planet, it should be ensured that each house must contain 8 marks both auspicious and inauspicious places put togather. Any difference in the total number will be the indication of some error and the same may be identified. by rechecking the steps carried over.
On the similar lines, the Ashtakavargas of the other planets should be developed. Let us take this exercise by noting the Rekhaprada (benefic lines) planets in respect of Moon's Ashtakavarga as has been narrated by the Sage in the preceding Adhyaya. This could be summerised as follows:
| From the | Number of Positions | |
| Sun | : 3rd, 6th, 7th, 8th, 10th, 11th | 6 |
| Moon | : 1st, 3rd, 6th, 7th, 10th, 11th | 6 |
| Mars | : 2nd, 3rd, 5th, 6th, 9th, 10th, 12th | 7 |
| Mercury | : 1st, 3rd, 4th, 5th, 7th, 8th, 10th, 11th | 8 |
| Jupiter | : 1st, 4th, 7th, 8th, 10th, 11th, 12th | 7 |
| Venus | : 3rd, 4th, 5th, 7th, 9th, 10th, 11th | 7 |
| Saturn | : 3rd, 5th, 6th, 11th | 4 |
| Ascendant | : 3rd, 6th, 10th, 11th | 4 |
| Total auspicious positions | 49 | |
| As such, the inauspicious (dots) positions | 47 |
The remaining positions out of 12 in respect of each planet will belong to Bindu as has been displayed in case of the Sun and need not be exercised over here as it is quite simple to ascertain.
Similarly, an individual Ashtakavarga chart which is also known as Bhinnashtakavarga (B.A.V. hereinafter in short) of the Moon and other planets be worked out, firstly in respect of each planet and then a compound chart be drawn. Hence onward, we will restrict overselves to B.A.V. chart of each planet rather than drawing individual chart and then developing the compound B.A.V. chart.
B.A.V. Chart of the Moon :

| From the | : | Number of Positions |
| Sun | : 3rd, 5th, 6th, 10th, 11th | 5 |
| Moon | : 3rd, 6th, 11th | 3 |
| Mercury | : 3rd, 5th, 6th, 11th | 4 |
| Mars | : 1st, 2nd, 4th, 7th, 8th, 10th, 11th | 7 |
| Jupiter | : 6th, 10th, 11th, 12th | 4 |
| Venus | : 6th, 8th, 11th, 12th | 4 |
| Saturn | : 1st, 4th, 7th, 8th, 9th, 11th | 7 |
| Ascendant | : 1st, 3rd, 6th, 10th, 11th | 5 |
| Total auspicious positions | 39 | |
| As such, the inauspicious positions | 57 |
B.A.V. Chart of Mars:

| From the | : | Number of Positions |
| Sun | : 5th, 6th, 9th, 11th, 12th | 5 |
| Moon | : 2nd, 4th, 6th, 8th, 10th, 11th | 6 |
| Mars | : 1st, 2nd, 4th, 7th, 8th, 9th, 10th, 11th | 8 |
| Mercury | : 1st, 3rd, 5th, 6th, 9th, 10th, 11th, 12th | 8 |
| Jupiter | : 6th, 8th, 11th, 12th | 4 |
| Venus | : 1st, 2nd, 3rd, 4th, 5th, 8th, 9th, 11th | 8 |
| Saturn | : 1st, 2nd, 4th, 7th, 8th, 9th, 10th, 11th | 8 |
| Ascendant | : 1st, 2nd, 4th, 6th, 8th, 10th, 11th | 7 |
| Total auspicious positions | 54 | |
| As such the inauspicious positions | 42 |
B.A.V. Chart of Mercury :

| From the | : | Number of Positions |
| Sun | 1st, 2nd, 3rd, 4th, 7th, 8th, 9th, 10th, 11th | 9 |
| Moon | 2nd, 5th, 7th, 9th, 11th | 5 |
| Mars | 1st, 2nd, 4th,7th, 8th, 10th, 11th | 7 |
| Mercury | 1st, 2nd, 4th, 5th, 6th, 9th, 10th, 11th | 8 |
| Jupiter | 1st, 2nd, 3rd, 4th, 7th, 8th, 10th, 11th | 8 |
| Venus | 2nd, 5th, 6th, 9th, '10th, 11th | 6 |
| Saturn | 3rd, 5th, 6th, 12th | 4 |
| Ascendant | 1st, 2nd, 4th, 5th, 6th, 7th, 9th, 10th, 11th | 9 |
| Total auspicious positions | 56 | |
| As such, the inauspicious positions | 40 |
B.A.V. Chart of Jupiter :

| From the | : | Number of Positions |
| Sun | : 8th, 11th, 12th | 3 |
| Moon | : 1st, 2nd, 3rd, 4th, 5th, 8th, 9th, 11th, 12th | 9 |
| Mars | : 3rd, 5th, 6th, 9th, 11th, 12th | 6 |
| Mercury | : 3rd, 5th, 6th, 9th, 11th | 5 |
| Jupiter | : 5th, 8th, 9th, 10th, 11th | 5 |
| Venus | : 1st, 2nd, 3rd, 4th, 5th, 8th, 9th, 10th, 11th | 9 |
| Saturn | : 3rd, 4th, 5th, 8th, 9th, 10th, 11th | 7 |
| Ascendant | : 1st, 2nd, 3rd, 4th, 5th, 8th, 9th, 11th | 8 |
| Total auspicious positions | 52 | |
| As such, the inauspicious positions | 44 |
B.A.V. Chart of Venus

| From the | : | Number of Positions |
| Sun | : 1st, 2nd, 4th, 7th, 8th, 10th, 11th | 7 |
| Moon | : 3rd, 6th, 11th | 3 |
| Mars | : 3rd, 5th, 6th, 10th, 11th, 12th | 6 |
| Mercury | : 6th, 8th, 9th, 10th, 11th, 12th | 6 |
| Jupiter | : 5th,6th, 11th, 12th | 4 |
| Venus | : 6th, 11th, 12th | 3 |
| Saturn | : 3rd, 5th, 6th, 11th | 4 |
| Ascendant | : 1st, 3rd, 4th, 6th, 10th, 11th | 6 |
| Total auspicious positions | 39 | |
| As such, the inauspicious positions | 57 |
B.A.V. Chart of Saturn

| From the | : | Number of Positions |
| Sun | : 3rd, 4th, 6th, 10th, 11th, 12th | 6 |
| Moon | : 3rd, 6th, 10th, 11th, 12th | 5 |
| Mars | : 1st, 3rd, 6th, 10th, 11th | 5 |
| Mercury | : 1st, 2nd, 4th, 6th, 8th, 10th, 11th | 7 |
| Jupiter | : 1st, 2nd, 4th, 5th, 6th, 7th, 9th, 10th, 11th | 9 |
| Venus | : 1st, 2nd, 3rd, 4th, 5th, 8th, 9th | 7 |
| Saturn | : 1st, 3rd, 4th, 6th, 10th, 11th | 6 |
| Ascendant | : 3rd, 6th, 10th, 11th | 4 |
| Total auspicious positions | 49 | |
| As such, the inauspicious positions | 47 |
B.A.V. Chart of the Ascendant :

This Adhyaya (Chapter) embodied the subject of Trikona Shodhana (Triangular Reduction). After having drawn the Ashtakavarga chart for all the planets including the Ascendant, the next required step, in this ystem, is to apply certain reductions over these formats. The first of its kind being, of course, Trikona Shodhana. The Rashi Chakra (12 signs) encompasses four triads of triangular signs these are as follow :
i) First set of triangular signs : Aries, Leo, Sagittarius.
ii) Second set of triangular signs : Taurus, Virgo, Capricorn
iii) Third set of triangular signs : Gemini, Libra, Aquarius
iv) Fourth set of triangular signs : Cancer, Scorpio, Pisces.
Method of Trikona Shodhana :
The method of this type of reduction has been explained by the Sage in Shlokas 3 to 5 ibid which are intended to be applied differently, depending upon the various combinations of number of benefic Rekhas contained by the each sign of the concerned set of triangular signs. Let us take a critical look over the four triads of triangular signs in the Ashtakavarga of the Sun and then apply these principles.
The first step required over here is to locate the sign in which the Sun is posited in the birth chart and identification (counting) of first trine sing will commence from that very sign. Therefore, write down the twelve signs starting from that sign (the sign of the Sun) and then implant the other planets in the column of their respective signs of nativity. Thereafter, note down the number of Rekhas obtained by these signs in the Ashtakavarga of the Sun below each of them. Let us draw the Trikona Shodhana (reduction) Chakra accordingly.
Trikona Shodhana Chakra of the Sun's Ashtakavarga :
| Planets | Sun Mer | Rah | Ket | Mon Mar Jup | Ven Sat | Total Nos. | |||||||
| Signs | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 1 | 2 | 3 | 4 | -- |
| No. of Rekhas | 3 | 3 | 3 | 3 | 3 | 5 | 5 | 5 | 6 | 3 | 5 | 4 | 48 |
| After Reduction | 0 | 0 | 0 | 0 | 0 | 2 | 2 | 2 | 3 | 0 | 2 | 1 | 12 |
The Sun is posited in the Leo sign and this Leo sign thus becomes the part of first triangle and the other two signs being Sagittarius and Aries. These signs are having Leo (3), Sagittarius' (3) and Aries (6) Rekhas. Since the minimum in 3, it should deducted from all the three numbers leaving the balance as, 0, 0 and 3. Similarly, the second triangle will be that of Virgo (3), Capricorn (5) and Taurus (3). Here also 3 is the least number and on applying reduction of figure 3 to all, we get 0, 2 and 0 as the balance. Now coming to the 3rd triangle of Libra (3), Aquarious (5) and Gemini (5). Again we got the figure 3 as the least number and consequently, the reduced digits will be 0, 2 and 2. In the fourth triangle of Scorpio (3), Pisces (5) and Cancer (4) also, we get 3 as a least digit. By reducing it from all the three, the resultant number will be 0, 2 and 1.
The number as obtained after the reduction should be noted down below each sign as are shown in this Chakra. It may be noted that in all the four triads of Triangular signs, the first principle of the Shlokas 3 to 5 is applicable.
The second principle enjoined in these Shlokas is that in the trinal signs, if any sign is devoid of any Rekha, no reduction would be needed. Let us suppose, in the first triad of the triangular signs i.e. Aries, Leo and Sagittarious possess numbers 0, 3 and 6 respectively. Since '0', is the least digit in this triad, as the rule goes, it should be got reduced from all the three numbers and the application of which would result in virtually no reduction.
Now let us take on to the third principle embodied in these Shlokas which states that if all the number of the three signs of a particular trine are identical, even then these identical figures be got reduced from all of them. For example, in the 3rd trinal group of Triangular signs viz., Gemini, Libra, Aquarius, carry 2 Rekhas in each of them and hence, the deduction of the digit 2 will be carried out from all the three signs, leaving a balance of '0' in all the three cases. This principle be said in this manner that if number of Rekhas in all the three signs are equal, then all the numbers in the entire trinal group be eliminated (i.e. reduced to zero).
All the three principles enunciated in the Shlokas 3 to 5 ibid, can be summed up as follows:
(i)When dissimilar figure of Rekhas appear in a trinal group of three signs, reduce the lowest from all the three figures.
(ii)When any sign in a trinal group of signs is devoid of any Rekha, no reduction is necessary.
(iii)When number of Rekhas in all the three signs of the trinal group are equal, remove all the numbers (have it reduced to zero).
On completion of this Trikona Shodhana, other Shodhanas (reductions) are applied on these modified figures.