# Indian Discoveries And Inventions – Part V

**ASTRONOMICAL DEFINITIONS **

*Urdhvamadho apara poorvamihaadyam praahuridam samamandala manyath thadvadihotthara dakshinadikstham vrutthayugam vidisorapi thadvath *

Vertical circle passing through the west and east cardinal points is the first circle: this is called the samamandala. (This circle is the prime vertical. Another similar vertical circle (called the yaamyottara-vrutta) which passes through the north and south cardinal points is called the meridian.

**VATESWARA – VATESWARA SIDDHANTA 880 AD**

**TYCHO BRAHE REDUCTION OF ECLIPTIC ****DISCOVERED BY ACHYUTA PISHAROTI **

*Patonasya vidhostu kotibhujayorjive mithastadayet antyakshepasarahatam vadhamamum vikshepakotyaharet labdham vyasadaloddhrtam himakare svarnam, vipate vidhau yugmaayugmapadopage; vidhurayam spashto bhagole bhavet *

Multiply the tabular cosine and sine of the moon minus node and the product by the tabular versine of the maximum latitude of the moon. Divide this by the tabular cosine of the latitude at the particular moment and the quotient is to be divided again by the tabular radius. The result is to be added to or subtracted from the moon’s longitude, as the moon minus node is in an even or an odd quadrant, respectively. The true moon measured on the ecliptic is thus obtained.

**ACHYUTA PISHAROTI SPHUTANIRNAYA**

**EQUATOR **

*Khasvasthikaad dakshinatho akshabhaagow paathaa (la) samjnachha thathottharena naadyankitham vaishuvatham thaduktham vruttham bhagolasya khagolamadhye *

The sphere of the asterisms lie within the sphere of the sky. Great circle of the sphere of asterisms which lies towoards the south of the zenith by an amount equal to the degrees of local latitude and towards the north of nadir by the same amount and which is graduated with the division of nadis is the vishuvathvrutta. This circle is called the equator.

**VATESWARA SIDDHANTA 880 AD **

**6 O’CLOCK CIRCLE **

*Poorvaaparakshithija sangamayorgathamcha yaamyaadadha: palalavai:*

*kshithijaadvi lagnam soumyaadathopari samadruvamarga samstham unmandalam dinaniso: kshayavruddhikruthaath. *

Passing through the two points of intersection of prime vertical and horizon, lying below the south cardinal point by the degrees of local latitude, fastened to the horizon, and lying above the north cardinal point, passing through the north celestial pole, is the Unmandala, the cause of decrease and increase of the day and night. (This in modern astronomy is known as the 6’o clock circle.)

**VATESWARA SIDDHANTA 880 AD **

**CIRCLE OF DIURNAL MOTION **

*Harije parapoorva mandala dyujaavruthha visesha sinjinee udayaagraguno dyumandale bhoojyothavruttha kujaan tharaamsajeevaa: *

R sine of the arc of the horizon lying between the prime vertical and the diurnal circle of the planet is the R sine of agra (now known as the rising point of the planet) and the R sine of the degrees of diurnal circle lying between six o’ clock circle and the horizon is bhoojya (bhujya) which is termed as Earthsine.

**VATESWARA SIDDHANTA 880 AD **

**DAY RADIUS **

*Kraanthijyaa vargonaath thrijyaavargaath padam dyujeevaa syaath thrijyaakraanthi yaanthara samaasa ghaathasya moolam vaa *

Day radius is equal to the square root of the difference obtained by subtracting the squares of R sine of the declination from the square of the radius or the square root of the product of the difference and the sum of the radius and the R sine of the declination.

**VATESWARA SIDDHANTA 880 AD **

** **

**ECLIPTIC **

*Naaddyaahvavrutthaajathulaadilagnam jinaamsakairadakshinatho mrugaadow soumye seetha mandiraadaav apakramaakhyam thadusanthi vruttham *

Fastened to the so called nadivrutta or the equator at the points of Aries and Libra and lying 24 degrees of the south (of equator) at the first point of Capricon and 24 degrees to the north (of equator) at the first point of Cancer, there is a great circle called the apakrama vrutta (now known as the ecliptic)

**VATESWARA SIDDHANTA 880 AD **

**DAY DIAMETER **

*Vishuvajyaa aayaa mardha varga vislesha moolamavalambaka: kranthithrijyaakruthyo rantharapadam dvigunam dinavyaasa *

Square the sine of latitude and deduct from the square of the radius. Its square root is the sine of the co-latitude (its arc being the co-latitude). Square the sine of the declination deduct from the square of the radius and find its root. Twice the result is the day diameter.

**PANCHASIDDHANTIKA 4-23 – VARAHA MIHIRA 505 AD**

**SETTING POINT OF ECLIPTIC **

*Praachyaam kuja apakrama vrutthasanga praaglagnamaahu (paritho asthalagnam) (lagnaadbhaveth) sa (pta) ma (raa) si (ra) stha thasyaa (stha) kaalo abhyudayosya bhooyath *

Point of intersection of horoizon and the ecliptic in the eastern half of the celestial sphere is called praglagna. I.e. the rising point of ecliptic; the same in the western half is called astalagna, known as setting point of ecliptic.

**VATESWARA SIDDHANTA 880 AD **

**RISING – SETTING LINE **

*Vyaasaardha vrutthe antharam ethayo: syaaccharaardha jeevaa parapoorvayosthath agraagrayoryad harijenibaddham soothram grahaanaam udayaastha samjnam *

The arcual distance between the six o’clock circle and the horizon measure, along the R circle trijyavrutta known as great circle of the celestial sphere, supposed to be of radius 3438’ (minute of angle) is the charardhajya. It is called the R sine of the Ascensional difference. A thread tied to the extremities of the agra on the eastern and western halves of the horizon is called the udayaastasutra. (In moderen astronomy it is known as the rising – setting line of planets).

**TESWARA SIDDHANTA 880 AD**

**DAY RADIUS AND EARTHSINE **

*Kraanti thribhaantharajyaa dyujyaa vaa charadalajeevayaa hruthaa thrijyaa kshithi jeevaghnaa svaahoraathraardhajeevaa vaa *

Rsine of the difference between the three signs and the declination is also equal to the day radius. Day radius multiplied by earthsine and divided by the R sine of the Ascensional difference gives the day radius.

**VATESWARA SIDDHANTA 3(4)-3) – 880 AD **

**SUN’S PRIME VERTICAL **

*Urdhvamadho aparapoorvamihaadyam praahuridam samamandala manyath thadvathihottharadakshina dikstham vrutthayugam vidisorapi thadvath. *

Vertical circle passing through the west and east cardinal points is the first circle called samamandala or the prime vertical.

**VATESWARA SIDDHANTA- GOLA. 3-1, 2 – 880 AD **

**PARALLAX-I **

*Thithernathasya kramasinjanee hathaa khamadhya lagnaprabhavena sankunaa kshamaashadangkaabhi saraankanethrahrud vilambane syaad ghatikaadi vaa phalam. *

R sine of the hour angle at the amavasya multiplied by R sine of the altitude of the meridian ecliptic point and divided by 2954961 gives the parallax in ghatikas at mid eclipse (Sishyadhi vruddhi Tantra 6-8)

**LALLACHARYA SISHYADHI VRUDDHI TANTRA **

**PARALLAX-II **

*Thriraasijeevaa valanajyakaa hruthaa sileemukhai rankulathaam vrajanthi thaa: dvisankunaa drushtigathi: saraachalairvibhaajithaa lambana naadikaa phalam *

Radius and the valanajya when divided by 5, are converted into angulas. The R sine of driggati multiplied by 2 and divided by 75 gives ghatika of the parallax in longitude. (Sishyadhi vruddhi Tantra 13-11)

**LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD **

**PARALLAX-III **

*Nathakramajyaambara sankunighnaa syaallambanam thathvarase shuhrudvaa drukshepabhukthyanthara yoscha ghaatha: khabaanayugmaa kshihrutho nathi: syaath *

R sine of the hour angle multiplied by Rsine of altitude of the merdian ecliptic point and divided by 5625 gives parallax in longitude. The Difference of true motions of the Sun and the moon multiplied by the Rsine of drikshepa and divided by 2250 gives the parallax in latitude. (Sishyadhi vruddhi Tantra 13-12)

**LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD **

**APOGEE, PERIGEE AND ORBIT OF EARTH **

*Svochhaath shadbhaagaadhyadhiko yadaa thadaa bhavathi svaneechastha: doorenochhaga urvyaa: karnavasaannochhago nikate *

When a planet is at a distance of 6 signs from its apogee, it is said to be at the perigee or neecha. When a planet is at the apogee, it is farthest from the earth when at the perigee, it is nearest to the earth. This is so because of the length of the hypotenuse in each case (Sishyadhi vruddhi Tantra 14-10)

**LALLACHARYA SISHYADHI VRUDDHI TANTRA 700 AD **