# गणितशब्दावली

अक्ष -- Latitude - The term akṣa is an abbreviation of the complete term, akṣonnati, meaning the inclination of the Earth's axis to the plane of the celestial horizon, i.e., the latitude of the place

अक्षजीवा -- R sine of latitude

अक्षज्या -- R sine of latitude

अक्षांशः -- Local latitude in degrees

अक्ष्णयारज्जु -- The diagonal chord of rectangle or a square

अग्रा -- Amplitude at rising i.e., the arc of the celestial horizon lying between the east point where the heavenly body concerned rises; or the R sine thereof (sometimes called agrājyā), which is equal to the distance between the east-west line and the rising-setting of the heavenly body concerned

अङ्गुलम् -- 1. Digit, as a unit of linear measure (finger-breadth). 2. Unit of length, 1/24th of a cubit

अधिदिनम् -- Intercalary day

अधिमासः(क) -- Intercalary month; the intercalary months denote the excess the lunar (synodic) months over the solar months and thus the intercalary months in a yuga are the lunar months minus the solar months in the yuga

अधिमासशेषः -- Residue relating to the intercalary month, adhimāsa

अधिवर्ष -- Twelve intercalary months

अनादेश्यग्रहणम् -- The eclipse that are not to be predicted

अनुलोम -- Direct or anticlockwise

अनुष्टुप् -- A Sanskrit verse meter consisting of four quarter-verses of eight syllables each

अन्त्यज्या -- The current R sine difference, i.e., the R sine difference corresponding to the elementary arc occupied by a planet In Hindu trigonometry, the quadrant of a circle is divided into 24 equal parts called elementary arcs.

अन्त्यफलम् -- Maximum correction due to the mandocca or śīghrocca

अन्त्यफलज्या -- R sine of the maximum correction

अपक्रमः -- 1. Greatest declination. 2. Declination

अपक्रममण्डलम् -- Ecliptic

अपमा -- Declination

अपमण्डलम् -- Ecliptic

अमावस्या -- Day of conjunction of Sun and Moon i.e., New Moon day

अयतम् -- Rectangle

आयतचतुर्भुजम् -- Rectangle

अयतवृत्त -- Ellipse

अयनम् -- Northward or southward motion of a planet

अयनांशः -- Arc of the ecliptic intercepted between the vernal equinox and the zero point (as set by the Indian tradition)

अर्काग्रा -- Sun's amplitude at rising, or the R sine thereof

अर्ध -- Half

अर्धज्या -- R sine

अवनतिः -- Moon's true latitude as corrected for parallax

अवमरात्र -- Omitted lunar days or omitted tithis

अवमशेष -- Residue of the omitted lunar days or omitted tithis

अवमदिनम् -- Omitted lunar days or omitted tithis

अविशेषकलाकर्णः -- The distance (lit., hypotenuse) of a planet measured in minutes and obtained by the method of successive approximations

अंशः -- 1. Degree. 2. Part. 3. An upper vertex of a quadrilateral.

अश्वयुक् -- Month of Aśvina,

असकृत्कर्म -- Method of successive approximations

असवः -- Asus of the right ascension or the time in the asus of rising at the equator

असित -- 1. asita pakṣa i.e., the dark half of a lunar (synodic) month. 2. The measure of the unilluminated part of the Moon

असुः -- A unit of time equal to four sidereal seconds

अस्तः -- The setting of a heavenly body

अस्तमयः -- Diurnal or heliacal setting

अस्तमयोदयसूत्रम् -- R sine setting line

अस्तलग्नम् -- The setting point of the ecliptic

अहर्गणः -- 1. The number of days accumulated between a given epoch date and some desired date. 2. The number of mean civil days elapsed since the beginning of Kaliyuga (or any other epoch)

अहोरात्रम् -- 1. A day and night, a nychthemeron. 2. The day radius i.e., the radius of the diurnal circle

अहोरात्रवृत्तम् -- Diurnal circle

अहोरात्रार्धविष्कम्भ -- Semi-diameter of the diurnal circle (of a heavenly body, particularly the Sun) i.e., the day radius.

अहोरात्रासु -- The number of asus in a day and night i.e., 21600

आक्षदृक्कर्म -- Visibility correction due to local latitude

आबाधा (or अवबाधा, अवधा, अबधा, बधा) -- Segment of the base of triangle produced by the altitude on it; the projection of any slanting side on the horizontal

आयनदृक्कर्म -- Visibility correction due to ecliptic longitude

आयाम -- Breadth of an object; sometimes, length as opposed to breadth

इन्दुआत -- Ascending node of the Moon

इन्दूच्च -- The Moon's apogee i.e., the remotest point of the Moon's orbit

इल्लम् -- (Malayalam) Among Brāhmaṇas in Kerala, a family residence or estate

इषु -- 1. Arrow. 2. Height of an arc or segment of a circle

इष्ट -- 1. Given, desired or chosen at pleasure. 2. iṣṭagraha i.e., desired or given planet

इष्ठशङ्कु -- R cosine of the zenith distance of the Sun in any arbitrary position

उच्च -- The ucca of a planet is of two kinds - (a) mandocca i.e., the apex of slowest motion and (b) śīghrocca i.e., the apex of fastest motion

उच्चनीचपरिवर्त -- Anomalistic or synodic revolutions

उच्चनीचवृत्त -- Epicycle

उच्छ्रय (or उच्छ्रिति) -- Height of an object

उत्क्रमण (also known as उत्क्रमज्या) -- R versed sine

उत्तरायण -- Sun's northward journey from winter solstice to summer solstice

उत्वृत्त -- Equatorial horizon

उत्वृत्तशङ्कु -- R cosine of the zenith distance of the Sun as seen from a place on the equatorial horizon

उत्सेध -- Height of an object

उदगयन (उत्तरायण) -- Sun's northward journey from winter solstice to summer solstice

उदग्गोल -- Northern Hemisphere

उदय -- 1. The rising of a planet on the eastern horizon. 2. Heliacal rising of a planet. 3. udaya lagna i.e., the rising point of the ecliptic. 4. Addition, as in kṣayodayau i.e., subtraction and addition

उदयजीवा (also known as उदयज्या) -- R sine amplitude of the rising point of the ecliptic

उदयास्त-सुत्र -- 1. Straight line joining the rising and setting points of a celestial body on a horizontal diameter. 2. Line of intersection of diurnal circle and horizon

उदयास्तमय -- Heliacal rising and setting

उदिचि -- North-South line

उन्नतकाल -- 1. Time elapsed after the rising of a celestial body. 2. Distance from the horizon in time

उन्नतांश -- Complement of the zenith distance, or the R sine of that called unnatāṃśajyā

उन्मण्डल -- 1. Equatorial horizon. 2. Six o'clock circle

उपवृत्त -- A small circle parallel to the prime-vertical

उभयतःप्रौग -- Double Isosceles triangle; rhombus

उर्वी -- 1. Base of a triangle. 2. Earth

ऋक्कर्म -- Visibility corrections. There are three visibility corrections: (a) akṣadṛkkarma which is the measure of the arc of the ecliptic lying between the hour circle and the circle of position of the planet concerned, (b) ayanadṛkkarma which is measured by the arc of the ecliptic lying between the circle of celestial longitude and the hour circle of planet concerned and (c) a correction of 48' to be subtracted from the Moon's longitude or added to it according as the Moon is in the eastern or western hemispheres. These corrections having been applied to the true longitude of a planet, we obtain the longitude of that point of the ecliptic that rises on the local horizon simultaneously with the actual planet

ऋजुभुज -- Rectilinear figure

ऋण -- Subtracted, negative

ऋतु -- Season

कक्ष्या -- Orbit

कक्ष्यामण्डल (अल्सो क्नोwन् अस् कक्षवृत्त) -- Mean orbit of planet, deferent of concentric

कटपयादि -- An alphanumeric notational system for verbally representing numerals

कदम्ब -- Pole of the ecliptic

कदम्बप्रत -- Secondary to the ecliptic

कदम्बसूत्र -- Secondary to the ecliptic

करण -- 1. A handbook for astronomical computation or astronomical manual. 2. A time unit equal to half a tithi or the time during which the Moon gains 6° over the Sun 3. The name of one of the five principal elements of the Hindu calendar

करणी -- 1. A surd or non-square number; (lit., making). 2. The side of a rectilinear figure; the side of a square or rectangle. 3. The maker or producer of the required area.

कर्ण -- 1. Hypotenuse, lateral side. 2. Distance of planet from Earth

कला -- A time unit equal to one-sixtieth of a muhūrta. 2. In the Jyotiṣa vedāṅga, a time unit equal to 201/20 of a ghaṭikā. 3. Minute of Arc

कलार्धजा -- The 24 R sine differences in terms of minutes

कलियुग -- The last of the four ages in a mahāyuga, equal to 432,000 years. Indian cosmology holds that the current Kaliyuga began on 18 February 3102 BCE

कल्प -- 1. A lifetime of the universe, conventionally equal to 4,320,000,000 years. 2. A period of 1000 yugas. 3.The Vedāṅga of ritual practice

कालांश -- Degrees indicating time

काह -- A day of Brahmā known as a Kalpa

कु -- 1. Earth. 2. Base of a triangle

कुज -- Mars

कुज्या -- Earth-sine. The distance between the rising-setting line and the line joining the points of intersection of the diurnal circle and the six o'clock circle, or the R sine thereof

कुवायु -- Terrestrial wind

कूदिन -- Civil days or Terrestrial days

कृति -- Square

कृत्तिका -- The nakṣatra of Kṛttikā

केन्द्र -- 1. Anomaly. The kendra is of two kinds, mandakendra and śīghrakendra. The mandakendra of a planet is equal to the 'longitude of the planet minus the longitude of the planet's mandocca i.e., the planet's apogee', where as the śīghrakendra of a planet is equal to the longitude of the planet's śīghrocca i.e., the apex of fastest motion, minus the longitude of the planet. 2. Centre

कोटि (कोटी) -- 1. Vertical/perpendicular side of right-angled triangle. 2. Complement of the bhuja

कोटिज्या -- Cosine, R cosine

कोटिफल -- The result obtained by multiplying the R sine of the koṭi due to the planet's kendra by the tabulated epicycle and dividing the product by 80

कोण -- Angle, corner

कोणमण्डल (कोणवृत्त) -- Intermediary vertical circle

कोणशन्कु -- 1. R cosine of the zenith distance of the Sun when the azimuth measured from the East-West line is 45°. 2. R sine of the altitude from the intermediary vertical circle, koṇavṛtta

कोणशन्कुतल -- Base of the koṇaśanku

कोष्ठक -- A set of tables for astronomical computation

क्रम -- Serial order

क्रमज्या -- 1. Sine or Chord; (lit. bowstring.) 2. R sine (Radius × Sine). The R sine difference corresponding to the twenty four equal divisions of a quadrant

क्रान्ति -- Declination

क्रान्तिज्या -- R sine of the declination of a celestial body

क्रान्तिमण्डल -- Ecliptic

क्रिय -- The zodiacal sign, Aries

क्वावर्त -- Rotations of the Earth

क्षयमास (अंहस्पतिमास) -- A candramāsa lost in the process of intercalation

क्षययह (उनह) -- A lost tithi or a tithi containing two consecutive Sunrises

क्षितिज -- 1. Mars. 2. Horizon (kṣitija vṛtta)

क्षितिजा (also known as क्षितिज्या) -- Earth-sine. The distance between the rising-setting line and the line joining the points of intersection of the diurnal circle and the six o'clock circle, or the R sine thereof

क्षिप्ति -- Celestial latitude

क्षिप्तिलिप्तिकाः -- The minutes of the celestial latitude

क्षेत्र -- Closed figure

क्षेत्रगणित -- Geometry

क्षेत्रफल -- Area

क्षेप -- 1. Additive or subtractive quantity/correction. 2. Celestial latitude, see under vikṣepa

-- 1. Void. 2. Sky

खगोल -- Sphere of the sky

खण्डग्रहण -- Partial eclipse

खमध्य -- Middle of the sky

खातफल -- Volume of a pit or excavation

गच्छ -- In Jainism, a lineage of teachers and pupils

गणित -- 1. Computation, calculation; mathematics in general. 2. The mathematical component of astronomy and astrology

गत -- Traversed, elapsed, past, preceding

गति -- Motion, generally used in the sense of daily motion of the planets

गत्यन्तर -- Motion-difference

गन्तव्य -- To be traversed; to come, succeeding

गुणक -- Multiplier

गुर्वक्षर -- Long syllable

गुर्वब्द -- Jovian year

गोत्र -- Among Brāhmaṇas, a lineage tracing its descent to one of the legendary sages of Hinduism

गोल -- 1. Sphere. 2. Celestial sphere. 3. Hemisphere; northern or southern hemispheres 4. Spherics

गोलयन्त्र -- Automatic sphere-model of the bhagola

ग्रह -- Planet

ग्रहक्षितिज -- A great circle whose poles are situated at a planet

ग्रहण -- Eclipse

ग्रहणमध्य -- Middle of the Eclipse

ग्रास -- 1. Measure of the eclipse. 2. Erosion by overlapping. 3. Common portion of two intersecting circles; the largest width thereof

ग्राहक -- The eclipsing body; the eclipser

ग्राहकार्ध -- Half the diameter of the eclipsing body

ग्राह्य -- The eclipsed body

ग्राह्यबिम्ब -- The disc of the eclipsed body

ग्राह्यमण्डल -- The centre of the eclipsed body

घटिका (अल्सो क्नोwन् अस् घटी), -- 1. A time unit equal to one-sixtieth of a day, 24 minutes

घटी -- A unit of time equal to 24 minutes

घनगोल -- Solid sphere

घनफल -- Volume

घनभूमध्य -- Earth's centre

घात -- Product; multiplication

घातक्षेत्र -- Diagrammatic representation of a multiplication product

चक्र -- 1. Circle. 2. Twelve signs or 360°

चक्रलिप्ता -- The number of minutes of arc in a circle, i.e., 21600

चक्रवालवृत्त -- Annulus

चक्रार्ध -- Half of a circle, i.e., 180°

चन्द्रकर्ण -- Distance of the Moon from the Earth

चन्द्रभगण -- Revolutions of the Moon

चन्द्रह -- Time taken by the Moon to overtake the Sun by 12° beginning from the zero point of the ecliptic (as set by the Indian tradition)

चन्द्रोच्च -- Moon's apogee

चर -- Ascensional difference. It is defined by the arc of the celestial equator lying between the six o'clock circle and the hour circle of a heavenly body at rising

चरजीवार्ध -- The R sine of the ascensional difference

चरज्या -- The R sine of the ascensional difference

चरदल -- Ascensional difference. It is defined by the arc of the celestial equator lying between the six o'clock circle and the hour circle of a heavenly body at rising

चरपाण -- The asus of ascensional difference

चरफल -- Correction due to ascensional difference

चरसंस्कार -- Latitude correction in the celestial longitude of a planet

चरासु -- The asus of ascensional difference

चलकेन्द्र -- The longitude of the planet's śīghrocca i.e., the apex of fastest motion, minus the longitude of the planet

चलकेन्द्रफल -- Correction due to the planet's śīghrocca

चलोच -- Apex of fastest motion.

चान्द्रमास (सषिमास) -- Lunar month or Lunation

चान्द्रवर्श -- Twelve lunar months

चाप -- Arc

चापक्षेत्र -- Segment

चापज्यार्ध (ज्या) -- R sine

चापभाग -- An element of arc of elementary arc, i.e., one of the twenty four equal divisions of a quadrant. The R sine differences for these have been tabulated by Aryābhaṭa I

चापित -- Converted into (or reduced to) the corresponding arc

चैत्र -- The name of the first month of the year

छन्दस् -- Prosody or poetic metrics. One of the six Vedāṅgas

छाया -- 1. Shadow. 2. The R sine of the zenith distance

छायाकर्ण -- Hypotenuse of the right-angled triangle formed with the gnomon and the gnomonic shadow cast by the Sun, being the other two sides

छायाभुज -- Length of the perpendicular from the end of the gnomic shadow to the East-West line

जन्य -- Rational right triangle or rectangle from which other rational figures are to be obtained; a figure with rational sides

जातक -- Genethlialogy; the practice or study of casting nativity horoscopes

जाति -- Hereditary social and occupational group, often translated caste

जात्य -- A rational right-angled triangle or any rectilinear figure with rational sides

जिवाभुक्ति -- True daily motion derived with the help of the table of R sine differences

जीवा -- 1. Sine or Chord; (lit. bowstring.) 2. R sine

जूक -- Sign Libra

ज्ञाति -- Hereditary social and occupational group, sometimes a subdivision of jāti and sometimes synonymous with it

ज्या -- 1. Sine or Chord; (lit. bowstring.) 2. R sine (Radius × Sine). The R sine difference corresponding to the twenty four equal divisions of a quadrant

ज्यार्ध (ज्या) -- R sine

ज्योतिष -- Astronomy and astrology. One of the six Vedāṅgas

तन्त्र -- A type of astronomical treatise

तम(स्) -- Section of Earth's shadow cone at the Moon's distance

तमोमूर्ति -- The Moon's ascending node

तमोविष्कम्भ -- Diameter of shadow, i.e., diameter of the Earth's shadow cone at the Moon's distance

ताजिक -- An Islamic form of horoscopic astrology

तात्कालिक -- momentary, instantaneous; (lit., at that time)

ताराग्रह -- Star planets, i.e., the planets Mars, Mercury, Jupiter, Venus and Saturn

ताराग्रहस् -- Planets: Mercury, Venus, Mars, Jupiter and Saturn

तिथि -- A lunar day, or one-thirtieth of a synodic month

तिर्यण्मानी -- 1. The transverse side of a quadrilateral, the horizontal side. 2. The transverse measurer

तुला -- Sign Libra

तुल्यचतुर्भुज -- 1. Square or Rhombus. 2. Quadrilateral with all four sides equal

त्रिज्या (also known as त्रिभज्या) -- Radius or 3438', literally the R sine of the three signs (or an arc of 90°)

त्रिभुज -- Triangle

त्रिसम -- 1. Equilateral triangle. 2. Trapezium with three equal sides

त्रैराशिक -- Rule of three quantities, simple proportion

त्र्यस्र -- Triangle, more specifically a right-triangle

दक्षिणायन -- Sun's southward motion from summer solstice to winter solstice

दण्ड -- A punctuation mark in the form of a vertical stroke

दर्शनसंस्कार -- Visibility corrections. There are three visibility corrections: (a) akṣadṛkkarma which is the measure of the arc of the ecliptic lying between the hour circle and the circle of position of the planet concerned, (b) ayanadṛkkarma which is measured by the arc of the ecliptic lying between the circle of celestial longitude and the hour circle of planet concerned and (c) a correction of 48' to be subtracted from the Moon's longitude or added to it according as the Moon is in the eastern or western hemispheres. These corrections having been applied to the true longitude of a planet, we obtain the longitude of that point of the ecliptic that rises on the local horizon simultaneously with the actual planet

दिक्ज्या -- R sine of the azimuth measured from the East point

दिन -- Day

दिनगण -- 1. The number of days accumulated between a given epoch date and some desired date. 2. The number of mean civil days elapsed since the beginning of Kaliyuga (or any other epoch)

दिनगत -- Time of day passed/elapsed

दिनदलान्त्या -- āntyā at midday

दिनशेष -- Time until sunset

दिनान्तोदयलग्न -- The rising point of the ecliptic at Sunset

दिनार्ध -- Half day

दृक्क्षेप -- 1. Ecliptic zenith distance or its R sine. Thus, the dṛkkṣepa is the zenith distance of that point of a planet's orbit which is the shortest distance from the zenith. This term is sometimes also used fro the R sine of that zenith distance. 2. The arc measuring on vertical to ecliptic between the zenith and the nonagesimal point

दृक्क्षेपज्या -- The R sine of the dṛkkṣepa

दृक्क्षेपमण्डल -- 1. Vertical circle through the central ecliptic point. 2. Secondary to ecliptic passing through the zenith

दृक्च्गाया -- Parallax

दृक्ज्या -- R sine of the zenith distance in any position

दृक्लम्बन -- Parallax in zenith distance

दृग्गति -- Arc of the ecliptic between the Sun or Moon and the celestial ecliptic point or its R sine value

दृग्गतिज्या -- R sine of dṛggati

दृग्गोल -- Visible celestial sphere

दृग्ज्या -- R sine of Meridian zenith distance or simply, the R sine of the zenith distance

दृङ्मण्डल -- 1. Vertical circle. 2. Circle passing through zenith and the planet

देशन्तर -- 1. The longitude of a place. It is either the distance of the place from the prime meridian or the difference between the local and standard times. 2. Longitudinal correction in the celestial longitude of a planet

देशन्तरघटी -- deśāntara, in ghaṭīs of the difference between the local and standard times

देशान्तरफल -- Correction due to the difference in longitude

दोर्ज्या -- R sine of longitude

द्युज्या -- 1. R cosine of the declination of a celestial body. 2. Radius of diurnal circle

द्युज्यामण्डल -- Diurnal circle

द्युज्यावृत्त -- Diurnal circle

द्युदलशन्कु -- R sine altitude at midday

द्यूगण -- 1. The number of days accumulated between a given epoch date and some desired date. 2. The number of mean civil days elapsed since the beginning of Kaliyuga (or any other epoch)

द्विसमभुज -- Isosceles triangle

धनु -- Arc

धनुःकाष्ठ -- Arc; (lit., bow-stick)

धनुर्भाग -- The element of arc or elementary arc, i.e., one of the twenty four equal divisions of a quadrant. The R sine differences for these have been tabulated by Aryābhaṭa I

धरा -- 1. Base of a triangle. 2. Earth

धर्म -- The Hindu doctrine of sacred law or righteousness; the moral and religious duties prescribed for humans

ध्रुव -- Pole of the celestial equator

ध्रुवप्रोत -- Secondary to the celestial equator

ध्रुवप्रोतवृत्त -- Declination circle

ध्रुवयष्टि -- Polar axis

ध्रुवसूत्र -- Declination circle

नक्षत्र -- 1. One of the twenty-seven or twenty-eight constellations that lie in the orbital path of the Moon. 2. An arc of the ecliptic with length 13° 20' , associated with one of the above mentioned lunar constellations. 3. An interval of time during which the Moon traverses an arc of 13° 20'. 4. Asterism

नक्षत्रदिवस (नक्षत्रदिन) -- Sidereal day

नक्षत्रमास -- Sidereal month

नतकाल -- Hour-angle measured in time

नतकालकोटिज्या -- R cosine of hour-angle

नतकालज्या -- R sine of hour-angle

नतकालेत्क्रमज्या -- R versed sine of hour-angle

नतज्या -- R sine of zenith distance

नतभाग -- Meridian zenith distance

नतभागज्या (नतज्या) -- R sine of zenith distance

नतांश -- Zenith distance

नति -- 1. Meridian zenith distance or the R sine of that. 2. Difference between the parallaxes in latitude of the Sun and the Moon i.e., latitudinal parallax

नभ -- Zero

नर -- Gnomon

नागरी (also called देव-नागरी) -- The name of the script most commonly used to write Sanskrit

नाडी -- Unit of time equivalent to 24 minutes

नाडीवलय -- Celestial equator

निरक्षजाः (असवः) -- Asus of the right ascension or the time in the asus of rising at the equator

निर्गम -- Annulus

नीच -- Perigee of epicycle or the the eccentric of the planet

नीचोच्चरेखा -- Line of apse

नीचोच्चवृत्त -- Epicycle

नीचोच्चवृत्त -- Epicycle

नेमि -- Part of an annulus

पक्ष -- 1. A school or faction. 2. One side of an equation; (lit., wing or side.) 3. Lunar fortnight, i.e., the period from new Moon to full Moon or from full Moon to new Moon. The period from new Moon to full Moon is called the light fortnight (or the light half of a lunar month - śuklapakṣa) and that from full Moon to new Moon is called the dark fortnight (or the dark half of a lunar month - kṛṣṇapakṣa)

पञ्चाङ्ग -- A yearly calendar tracking the succession of various civil, liturgical, and astronomical time units

पदभा -- A gnomon shadow measured in units of feet; (lit., foot-shadow)

परकर्ण -- Third diameter of a cyclic quadrilateral obtainable by interchanging a pair of adjacent sides

परमक्रान्ति -- Greatest declination of the Sun, i.e., the obliquity of the ecliptic

परमक्षिप्ति -- Greatest celestial latitude of the Moon, i.e., inclination of he Moon's orbit

परमापक्रम -- Greatest declination, obliquity of the ecliptic

परमापक्रमगुणः -- The R sine of the Sun's greatest declination

परमापक्रमजीवा -- R sine of the greatest declination

परशङ्कु (also known as परमशङ्कु) -- R sine of the greatest altitude, i.e., R sine of the meridian altitude

परिणाह -- Periphery, circumference

परिधि -- Circumference

परिमण्डल -- Ellipse or Circle

परिलेख -- 1. Diagram. 2. Projection of eclipse

परिवर्त -- Revolution

पर्व -- 1. Time of conjunction or opposition of the Sun and the Moon. 2. Full Moon or the new Moon tithi. 3. An eclipse of the Sun and the Moon.

पर्वनाडी -- The nāḍīs of the full Moon or new Moon tithi (also called parva) which are to elapse at Sunrise on that day. In other words, the time in nāḍīs which is to elapse at Sunrise before the time of conjunction or opposition of the Sun and the Moon

पल -- 1. Latitude. 2. Unit of time equivalent to 24 seconds

पलकर्ण -- Hypotenuse of the right-angled triangle formed with the gnomon and the equinoctial shadow being the other two sides

पलज्या -- The R sine of the latitude

पलभ -- Equinoctial shadow of the gnomon at noon

पश्चार्ध -- The western half

पात -- 1. An astrologically significant event when the longitudes of the Sun and Moon add up to 180° or 360° (equivalently 6 or 12 zodiacal signs). 2. The ascending node of a planet's orbit on the ecliptic. 3. The circumference cum in-centre cum ortho-centre of an equilateral triangle

पातभाग -- The degree of longitude of the ascending node

पातरेखा -- The perpendiculars on the base and top of a trapezium fro the the point of intersection of its diagonals

पाती -- Arithmetic; (lit., board - for the dust board on which computations were written out)

पाद -- 1. A quarter-verse; (lit., foot.) 2. Ascending Node

पार्श्वमानी -- 1. The lateral side of a quadrilateral or the flank-side measurement. 2. The flank-side measurer

पुराण -- A sacred work on cosmology, mythology, and historical legend

पूर्ण -- Full, complete

पूर्णिमा -- Full Moon

पूर्वापरायत -- Directed east to west

पूर्वापरासूत्र -- East-West line

पृष्ठफल -- Surface area

पृष्ठ्या -- Line of symmetry, usually the east-west line

पौस्ण -- The nakṣatra, Revatī which is presided over by pūṣā

प्रक्रिया -- Process

प्रग्रहण -- First contact in an eclipse

प्रग्रास -- The beginning of an eclipse, i.e., the first contact

प्रति-वृत्त -- Eccentric circle of a planet

प्रतिपद् -- The first tithi of either half of the lunar month

प्रतिमण्डल (केन्द्रवृत्त) -- The eccentric circle of a planet

प्रतिलोम -- Retrograde. A planet is said to be in pratiloma when its motion is retrograde.

प्रभा -- The shadow of the gnomon

प्रवहवायु -- Provector wind

प्राक्कल्प -- The eastern hemisphere

प्राक्पश्चिमसुत्र -- East-West line

प्राग्लग्न (लग्न or प्राग्विलग्न) -- Rising point of the ecliptic

प्राण -- Unit of time equal to four sidereal seconds or one-sixth of a vināḍikā

प्रौग -- Triangle, typically an isosceles triangle. (The fore-part of the shaft of a chariot that is triangular in shape)

बव -- The name of the five movable karaṇa, the karaṇa being one of the five important elements of the Hindu calendar

बाण -- 1. Arrow. 2. Height of an arc or segment of a circle

बाहु -- 1. The base of a right angled triangle. 2. The bāhu (or bhūja) corresponding to a planet's anomaly or to any arc/angle

बाहुफल -- Correction due to the mandocca or śigrocca of a planet

बिम्ब -- Disc or orb of a planet

बीज -- 1. Algebra. 2. A conversion constant to adjust astronomical parameters; (lit., seed)

ब्रह्मदिवस -- A day of Brahmā, a kalpa

-- 1. Asterism. 2. Sign

भगण -- The revolution number of a planet, i.e., the number of revolutions that a planet performs around the Earth in a certain period

भगोल -- Sphere of asterisms, with its centre at the Earth's centre

भचक्र -- Circle of the asterisms

भपञ्जर -- Circle of the asterisms

भपरिणाह -- Circumference of the circle of the asterisms

भभ्रम -- Revolutions of fixed stars

भाग -- 1. Degree. 2. Part

भिन्नदिक्क -- Unlike direction

भुक्तकाल -- Elapsed time

भुक्ति -- Motion or daily motion

भुक्तियोग -- Sum of daily motions

भुक्तिविशेष -- Motion differences

भुज -- 1. Longitude. 2. Base of a triangle

भुजा -- Lateral side of a right angled triangle

भुजाज्या -- The R sine of bhuja (bhujā or bāhu)

भुजान्तर -- Correction for the equation of time due to the eccentricity of the ecliptic

भुजाफल -- Correction due to the mandocca or śigrocca of a planet

भू -- 1. Base of a triangle. 2. Earth

भूगोल -- Sphere of the Earth

भूगोलविष्कम्भ -- Diameter of the Earth

भूज्या -- Earth-sine. The distance between the rising-setting line and the line joining the points of intersection of the diurnal circle and the six o'clock circle, or the R sine thereof

भूताराग्रहविवर -- The distance between Earth and a star planet

भूदिन -- Civil days or Terrestrial days

भूदिवस -- Civil days or Terrestrial days

भूमि -- 1. Base of a triangle. 2. Earth

भेद -- Occultation of a star

भोग -- Motion

भोग्यकाल -- Time to pass or expend

भोग्यखण्ड -- Tabular difference of R sine, etc. to be passed in the meridian

मकर -- Capricorn

मण्डल -- Circle, revolution

मध्य -- 1. Centre, middle. 2. Mean. 3. Middle term in a series. 4. Zenith distance of ecliptic point

मध्यग्रह -- Mean planet

मध्यच्छाया -- The midday shadow of the gnomon

मध्यजिवा -- The R sine of the zenith distance of the meridian ecliptic point

मध्यज्या -- Meridian sine, i.e., R sine of the zenith distance of the meridian ecliptic point

मध्यमलम्बन -- 1. Parallax in zenith distance. 2. Mean Altitude

मध्यमसवन -- Mean solar day

मध्यर्क्रान्ति -- Declination of the place of a planet on the ecliptic

मध्यलग्न -- Meridian ecliptic point

मध्यलग्नशन्कु -- R cosine of the meridian ecliptic point

मध्यस्फुट -- True mean motion of a planet

मध्याभुक्तिः -- Mean daily motion

मध्याह्नच्छायाकर्ण -- Hypotenuse of right-angled triangle, two sides of which are the gnomon and the midday shadow

मनु -- A period of time equal to 72 yugas

मन्द -- 1. The inequality in a planet's orbital motion that depends on its position with respect to the stars, analogous to zodiacal anomaly. (lit., slow). 2. Slow, apex of slow motion

मन्दकर्ण -- Hypotenuse associated with mandocca

मन्दकेन्द्रज्या -- R sine of the mandakendra

मन्दगतिफल -- Correction to the mean motion of a planet

मन्दपरिधि -- Circumference of the manda epicycle

मन्दफल -- Equation of the centre

मन्दफलज्या -- R sine of the equation of the centre

मन्दवृत्त -- manda epicycle

मन्दस्पष्टगति -- Mean motion of a planet corrected by mandagatiphala

मन्दस्फुट -- 1. Planet's longitude corrected for the equation of centre. 2. Mean motion of a planet corrected by mandagatiphala

मन्दस्फुटगति -- Mean motion of a planet corrected by mandagatiphala

मन्दान्त्यफल -- Maximum correction due to mandocca

मन्दान्त्यफलज्या -- R sine of the maximum correction due to mandocca

मन्दांश -- The longitudes of the apogees of the planets in terms of degrees

मन्दोच्च -- Apogee or aphelion of a planet

मन्दोच्चकर्ण -- Hypotenuse associated with mandocca

मन्दोच्चफल -- Correction due to planet's mandocca

मन्वन्तर -- A cosmological time span equal to seventy-one mahāyugas or 306,720,000 years

महायुग -- A cosmological time span equal to 4,320,000 years

मही -- 1. Base of a triangle. 2. Earth

माणैक्यार्ध -- Sum of the radii of the eclipsing and the eclipsed bodies

मास -- Month

मीन -- Sign Pisces

मीमांसा -- The Vedāṅga of philosophical investigation of scripture; a division of Indian philosophy

मुख -- Face, top-side of an object or figure with more than three sides, especially the top or shorter/parallel side of a trapezium

मुहूर्त -- A time unit equal to one-thirtieth of a day

मूल -- 1. Square root. 2. Base text (on which an expository commentary is written)

मृग -- Sign Capricorn

मेष -- Sign Aries

मैत्र -- The nakṣatra, Anurādhā which is presided over by Mitra

मोक्ष -- The separation of the eclipsed body after an eclipse, the last contact, or the end of the eclipse

याम्य -- 1. The south direction which is presided over by Yama. 2. The southern hemisphere (yāmyagola). 3. The nakṣatra, Bhariṇi that is presided over by Yama

याम्योत्तरअ (याम्योत्तरवृत्त or याम्योत्तरमण्डल) -- The local meridian

यावत्तावत् -- In algebra, an unknown quantity; abbr. as yā; (lit., as much as so much)

युग -- 1. A calendar intercalation cycle. 2. A cosmological time interval, especially a mahāyuga. 3. A period of 4,320,000 years

युत -- Added; abbr. as yu in algebra

युति -- 1. Union 2. Junction

योग -- 1. An interval of time during which the combined motions of the Sun and Moon add up to 13° 20'; (lit., sum) 2. Conjunction in longitudes of two heavenly bodies. 3. Addition

योगतारा -- Junction-stars, being the prominent stars of the twenty-seven nakṣatras used by the Hindu astronomers for the study of the conjunction of the planets, especially of the Moon with them.

योगभाग -- The degree of longitudes of the junction-stars

योजन -- 1. A unit of distance, probably somewhere between five and ten kilometres. 2. A unit of distance. 8000 × 4 cubits. The length of a yojana has differed at different times. The yojana of Āryabhaṭa I and Bhāskara I is roughly equivalent to 7½ miles

योजनकर्ण -- The distance of a planet in terms of yojanas

योजनव्यास -- The diameter in terms of yojanas

रज्जु -- Perimeter

रवि -- The Sun

रविकर्ण -- Distance of the Sun from Earth

रविभगण -- Revolutions of the Sun

रविमास -- Solar month

रविवर्ष -- Solar Year

राशि -- Zodiacal sign or 30 °

राहुबिम्ब -- Diameter of the shadow cone of the Earth at the lunar orbit

रुण्ड -- Breadth (of an annular ring)

रूप -- 1. Known number; unity; abbr. as rū in algebra

लक्षज्या -- Sine, R sine when R = 120 units

लग्न -- The rising point of the ecliptic i.e., orient ecliptic point.

लघुज्या -- Calculations of R sine of arcs of 10°

लघ्वहर्गण -- Civil days between the end of one solar year and any date in the current year

लङ्का -- The hypothetical place on the equator where the meridian of Ujjain intersects it, i.e., place with 0° longitude and 0° latitude

लङ्कोदय -- Time of rising of the Signs at Laṅkā, i.e., right ascensions of the Signs

लम्ब(क) -- 1. The R cosine of the colatitude 2. perpendicular/altitude/vertical of a figure

लम्बकगुण -- The R sine of the colatitude

लम्बज्या -- The R sine of the colatitude

लम्बन -- Parallax in longitude; or, in particular, the difference between the parallaxes in longitude of the Sun and the Moon

लम्बांश -- Colatitude in degrees

लिप्त -- Minute of an arc

लिप्ताशेष -- The residue of the minute

वज्रभास -- Cross-multiplication

वर्ग -- 1. Square, in arithmetic or geometry; abbr. as va in algebra. 2. The first twenty-five consonants in the Sanskrit alphabet

वर्ण -- lit., colour. 1. One of the four major divisions of humanity in Hinduism. 2. A way of designating unknown quantities in algebra; different unknowns are referred to by the names of different colours

वर्षाधिप -- Lord of the year

वलन -- (lit. deflection) valana relates to an eclipsed body. It is the angle subtended at the body by the arc joining the north point of the celestial horizon and the north pole of the ecliptic (i.e., the angle between the circle of position and the circle of celestial longitude of the eclipsed body). valana is generally divided into two components: 1. akṣavalana and 2. ayanavalana. The akṣavalana is the angle subtended at the body by the arc joining the north point of the celestial horizon and the north pole of the celestial equator (i.e., the angle between the circle of position and the hour circle of the eclipsed body). The ayanavalana is the angle subtended at the body by the arc joining the north poles of the equator and the ecliptic (i.e., the angle between the hour circle and the circle of celestial longitudes of the eclipsed body). The valana is also defined as follows: The Great circle of which the eclipsed body is the pole is called the horizon of the eclipsed body. Suppose that the prime vertical, equator and the ecliptic intersect the horizon of the eclipsed body at the points A, B, and C respectively, towards the east of the eclipsed body. The the arc AB is called the akṣavalana, the arc BC is called ayanavalana, and the arc AC is called valana. valana is also called spaṣṭavalana

वलयाकारक्षेत्र -- Figure shaped like an annulus or ring

वसुधा -- 1. Base of a triangle. 2. Earth

वाक्य -- A celestial longitude value encoded in alphanumeric notation; (lit., sentence)

वार -- Day

वासव -- The nakṣatra, Dhaniṣṭhā which is presided over by Vasu

विक्षिप्ति -- Celestial latitude

विक्षेप -- Celestial latitude

विक्षेपज्या -- The R sine of celestial latitude

विक्षेपमण्डल -- Orbit of the planet

विक्षेपलिप्तिका -- The minutes of celestial latitude

विक्षेपांष -- The degrees of celestial latitude

वित्रिभ -- Nonagesimal or the point of the ecliptic having a longitude 1° - 90° where 1 is the longitude of the point of intersection of the ecliptic with the horizon

विंदफल -- Volume

विंदफल -- Volume

विदिक्क -- Contrary direction

विनाडिका -- A unit of time, being one-sixth of a ghaṭikā equivalent to 24 seconds

विन्मण्डल -- Orbit of planet

विपल -- A unit of time, being one-sixth of a ghaṭikā equivalent to 24 seconds

विमर्दार्ध -- Half of the duration of totality of an an eclipse

वियत् -- Zero

विलिप्ता (also known as विलिप्तिका) -- Second of an arc

विलोमविवर -- Difference of two planets, one direct and the other retrograde

विवर -- Difference

विशख -- The nakṡatra, Visākhā

विशेष -- The difference between diagonal and the side of a square, especially when expressed in terms of the side

विषमत्रिभुज -- A Scalene triangle

विषुवजीव -- R sine of latitude

विषुवत् (विषुवत् वृत्त) -- Celestial Equator

विषुवद्दिन -- The day of the equinox

विषुवद्दिनमध्याह्नच्छाया -- The equinoctial midday shadow

विष्कम्भ -- Diameter

विष्कम्भचक्रवाल -- Ellipse

वृति -- Perimeter

वृत्त -- 1. Circle of its circumference. 2. Epicycle

वृत्तपरिणाह -- Circumference of a circle

वृत्तपरिधि -- Circumference of a circle

वेग -- Velocity

वेदाङ्ग -- One of the six limbs, or supporting disciplines, of the sacred Vedas

वेध -- Depth

वैधृत -- An astronomical phenomenon when the sum of the (true) longitudes of the Sun and the Moon amounts to a circle (i.e., 360° or 12 signs)

वैश्व -- The nakṣatra, Uttarāṣāḍha that is presided over by Viśve Devāḥ

वैष्णव -- The nakṣatra, Śravaṇa that is presided over by Viṣṇu

व्यतिपात -- An astronomical phenomenon when the sum of the (true) longitudes of the Sun and the Moon amounts to half a circle (i.e.., 180° or 6 signs)

व्यासयोजन -- Diameter in terms of yojanas

व्योम -- Zero

शकाब्द -- The year of Śaka era

शक्रतारकम् -- The nakṣatra, Jyeṣṭhā that is presided over by Indra (Śakra)

शङ्कवर्ग -- The distance of the projection of a heavenly body on the plane of the celestial horizon from the rising setting line of the heavenly body

शङ्कु -- 1. Gnomon. 2. The R sine of the altitude of a heavenly body

शङ्कुवेध -- Observations by the gnomon

शङ्खवृत्त -- A figure resembling the longitudinal section of a conch-shell

शर -- 1. Arrow. 2. R versed sine. 3. Celestial latitude. 4. Height of an arc or segment of a circle

शषि -- The Moon

शषिदिवस (चान्द्रदिन) -- Lunar day

शास्त्र -- Learned discipline, science

शीघ्र -- The inequality in a planet's orbital motion that depends on its position with respect to the Sun, analogous to synodic anomaly; (lit., fast)

शीघ्रकेन्द्र -- The śīghra anomaly

शीघ्रकेन्द्र -- The longitude of the planet's śīghrocca i.e., the apex of fastest motion, minus the longitude of the planet

शीघ्रकेन्द्रकोटिज्या -- R cosine of the śīghra anomaly

शीघ्रकेन्द्रज्या -- R sine of the śīghra anomaly

शीघ्रगतिफल -- Second correction to mean motion of planet

शीघ्रपरिधि -- Circumference of the śīghra epicycle

शीघ्रफल -- Second correction to mean longitude

शीघ्रफलज्या -- R sine of the second correction to mean longitude

शीघ्रवृत्त -- śīghra epicycle

शीघ्रशीघ्रोच्च -- śīghra epicycle

शीघ्रोच्च -- Apex of fastest motion, śīghra apogee

शीघ्रोच्चकर्ण (also known as शीघ्रकर्ण) -- It is equal to (R±Rsin(k))2+(Rsin(b)) 2−−−−−−−−−−−−−−−−−−−−−−−√ where R=3438′, k is koṭi and b is bhuja due to śīghrakendra

शीघ्रोच्चफल -- Correction due to the planet's śīghrocca

शुद्धि -- 1. Gain of the lunar reckoning over the Solar at the beginning of the lunar year. 2. Mean heliocentric position; for superior planets, mean position of the Sun

शुन्य -- Void

शुल्ब -- A measuring cord; ritual geometry for altar construction

शृङ्गाटक -- 1. Arrow. 2. Height of an arc or segment of a circle

शृङ्गोन्नति -- 1. Triangle. 2. Some form of four-sided figure, tetrahedron

श्रुति -- Sacred texts ascribed to divine revelation, such as the Vedas; (lit., hearing)

श्रेढीक्षेत्र -- Diagrammatic representation of mathematical series

श्रोणि -- A lower vertex of a quadrilateral or triangle

श्लोक -- Verse, especially a verse in anuṣṭubha meter

षडश्रि -- Tetrahedron

सकृत -- By the application of the rule only once (i.e., without the application of the method of successive approximation)

सङ्क्रान्ति -- 1. The moment when the Sun enters a zodiacal constellation (rāśi). 2. Last day of solar month

सन्धि -- The inter-space between the foot of an altitude and the foot of the flank-side from whose tip the altitude is drawn, usually in a quadrilateral

सपाटचन्द्र -- Longitude of the Moon with respect to the nearer node of the lunar orbit

सपाटसूर्य -- Longitude of the Sun with respect to the nearer node of the lunar orbit

सम -- North point of the horizon

समकल -- The planets are said to be samakala when they are either in conjunction or opposition in longitude

समकोष्ठमिति -- Area, a measure equal to unit squares in a figure

समचक्रवाल -- Circle

समचतुर्भुज -- 1. Square or Rhombus. 2. Quadrilateral with all four sides equal

समदलकोटि -- Altitude

समपरिणाह -- Circumference of a circle

समप्रोत -- Secondary to prime vertical

समबाहु -- Equilateral figure

सममण्डल (also known as समवृत्त) -- The prime vertical

समरेखा -- The meridian

समलिप्तेन्दु -- The longitude of the Moon for the time of opposition or conjunction of the Sun and the Moon

समशङ्कु -- 1. R cosine of the zenith distance of the Sun when it is on the prime-vertical. 2. R sine of the altitude from prime vertical

समसूत्र -- Secondary to the prime-vertical

समानलम्ब (or समलम्ब) -- A quadrilateral with the altitudes equal; trapezium

सम्पर्क -- 1. The sum of the diameters of the two bodies in contact. 2. Used in the sense of the sum of the two diameters of the eclipsed and eclipsing bodies

सम्पर्कार्ध (also known as सम्पर्कदल) -- Half the sum of the diameters of the eclipsed and eclipsing bodies

सम्पात -- Point of intersection

सम्पूर्वापरः शङ्कुः -- The R sine of the prime vertical altitude (of the Sun)

सर्वग्रास -- Total eclipse

सवनदिन -- Civil days or Terrestrial days

सवनह -- Civil days or Terrestrial days

सव्य -- Clockwise

संसर्प -- An intercalary month preceding a kṣayamāsa

संस्कृत -- Corrected

सायक -- 1. Arrow. 2. Height of an arc or segment of a circle

सार्पमस्तक -- Name of an astronomical phenomenon, one of the vyatipātas

सावनमास -- 30 civil days

सित -- 1. The measure of the illuminated part of the Moon's disc; the phase of the Moon. 2. The light half of the lunar month (sitapakṣa). 3. Venus

सितपक्ष -- The light or bright half of a lunar month

सितमान -- The measure of the illuminated part of the Moon's disc

सिद्धान्त -- Technical treatise; in particular, a comprehensive treatise on astronomy

सूची -- The inner, outer or middle diameter of an annular ring

सूचीक्षेत्र -- 1. Triangle got by producing the flanks of a quadrilateral till they meet. 2. The pyramid or cone got by producing the lateral faces of the frustum of a pyramid or cone

सूत्र -- A rule or algorithm; (lit., thread)

सोम -- A ritual beverage used in some ancient Vedic sacrifices

सौम्य -- 1. North. The northern (hemisphere). 2. Mercury

सौरदिन -- Solar day

सौरमास -- 1. Time taken by the Sun to traverse each of the zodiacal constellations (rāśi). 2. Solar month

सौरसंवत्सर -- Solar year

सौरसंवर्ष -- Solar year

सौरि -- Saturn

स्थित्यर्ध -- Half the duration (of an eclipse)

स्थित्यर्धनाडिका -- Half the duration (of an eclipse) in terms of nāḍīs

स्थूल -- Gross, approximate

स्पर्श -- First contact of an eclipse

स्फुट -- True or corrected

स्फुटक्रान्ति -- Declination of planet's centre

स्फुटग्रह -- True planet

स्फुटभुक्ति -- True (daily) motion

स्फुटभूपरिधि -- Circumference of the Earth measure parallel to the equator at a specified latitude

स्फुटभोग -- True motion

स्फुटमध्य -- 1. True mean motion of a planet. 2. The true-mean planet. 3. The true-mean longitude of a planet

स्फुटयोजनकर्ण -- The true distance of a planet in terms of yojanas

स्फुटलम्बन -- Parallax in longitude; or, in particular, the difference between the parallaxes in longitude of the Sun and the Moon

स्फुटविक्षेप -- Celestial latitude corrected by parallax

स्फुटवृत्त -- True or corrected epicycle

स्मृति -- Sacred texts ascribed to human authorship; (lit., remembering)

स्वदेशभूमिवृत्त -- The local circumference of the Earth, i.e., circumference of the local circle of latitude

स्वदेशभोदय -- Time of rising of the zodiacal signs at the local place, or oblique ascensions of the zodiacal signs

स्वदेशाक्ष -- The latitude of the local place

स्वदेशोदय -- Time of rising of the zodiacal signs at the local place, or oblique ascensions of the zodiacal signs

हरिज -- Horizon

हस्त -- Cubit, measure of length

हऽय -- (Arabic) Islamic astronomy, particularly its geometric models

हृति -- Hypotenuse

होरा -- Unit of time equivalent to 1/24th of one day and night period

## टीका

स्रोतम् : Glossary: Sanskrit Technical Terms

Terms and definitions collated from the following sources:

• Plofker, K. 2009. Mathematics in India. Princeton: Princeton University Press.
• Sarasvati Amma, T. A. 1979. Geometry in Ancient and Medieval India. Delhi: Motilal Barnarsidass.
• Somayaji, D. A. 1971. A Critical Study of the Ancient Hindu Astronomy in the light and language of the modern. Dharwar: Karnataka University.
• Subbarayappa, B. V. and K. V. Sarma. 1985. Indian Astronomy: A Sourcebook. Bombay: Nehru Centre.
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