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NILAKANTA - TANTRA SANGRAHA 1444 AD ista-dohkotidhanushoh svasamipasamirate jye dve saavayave nyasya kuryaad unaadhikam dhanuh dvighna talliptikaptaikasarasailasikhindavah nyasyacchedaaya cha mithastatsamskaaravidhitsaya anyasyam atha taam dvighnaam tathaa syam iti samskriti: santha te krtasamskare svagunau dhanusas tayo:   Placing the sine and cosine chords nearest to the arc, whose sine and cosine chords are required, get the arc difference to be subtracted or added. For making the correction, 13,751 should be divided by twice the arc difference in...

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PUTHUMANA SOMAYAJI - KARANA PADDHATI 1450 Anyonya kotihathayorabhimatha gunayosthrijeejavayaa hathayo: yogaviyogow syaathaamabhimathagunachaapa yogavivaragunow   The sum of the products of Sin A and Cos B and when angles are exchanged, Sin B and Cos A, gives the Sin of the sum of the angles. Similarly the difference of the above gives the value of the sin of angular difference. Sin (A+B) = Sin A Cos B+Cos A Sin B And Sin (A-B) =...

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BHASKARA II - LILAVATI 1114 AD   Jyaavyaasayogaanthara ghaathamoolam vyaasasthadoono dalitha: sara: syaath vyaasaaccharonaacchara sangunaa cha moolam dvinighnam bhavatheeha geevaa yeevaardhavarge sarabhaktha yukthe vyaasapramaanam pravadanthi vrutthe   When the sum and differences of diameter and the chord are multiplied, and their square root is taken and if half of that is subtracted from the diameter, the arrow is obtained. The difference of diameter and the arrow multiplied with the arrow, twice the square root of...

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BHASKARA II - LILAVATI 1114 AD   Vyaasaabdhighaathayuthamourvikayaa vibhaktho jeevangghri panchagunitha: paridhesthuvarga: labdhonithaath paridhivarga chathurtha bhaagaadaapte pade vruthidalaath pathithedhanu: syaath.   One fourth of five times the chord multiplied with square of circumference divided by four times the diameter added with the chord. This value is subtracted from one fourth of the square of circumference. Square root of this is taken and subtracted from half of the circumference to get the arc....

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ARYABHATTA I - ARYABHATEEYA 499 AD   Paridhe: shadbhaagajyaa vishkambhaardhena saa thulyaa   The chord of one sixth of circumference is equal to the radius of that circle....

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PUTHUMANA SOMAYAJI - KARANA PADDHATHI - 1450 AD   Svalpachaapaacchaghanashashta bhaagatho vistaraardhakruthir- bhaktha varjitham sishtachaapamihasinjanee bhaveth thadyuth oalpaka gunoasakruthdhanu:   The chord of an arc of a circle is obtained from the result of the cube of the length of the arc divided by six times the cube of radius and subtracted from the arc. This can be mathematically presented as follows: Chord (R Sine ) = s - (s3 / 6r3). Here length of...

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BHASKARACHARYA II - LILAVATI - 1114 A.D   Vrutthakshethre paridhigunitha vyaasapaada: phalam thath kshunnam vedairupari paritha: kandukasyeva jaalam golasyaivam thadapi cha phalam prushtajam vyaasanighnam shadbhirbhaktham bhavathi niyatham golagarbhe ghanaakhyam   When circumference is multiplied with diameter and that result divided by 4, that will give the area of a circle. This when multiplied with 4 gives the surface area of the globe which is like surface of a ball. This when multiplied with diameter and divided...

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PUTHUMANA SOMAYAJI - KARANAPADDHATI 1450 AD   Vyaasaath vanasangunithaath pruthagaaptam thryaadyayugvimoola ghanai: thrigunavygaase svamrunam kramasa: kruthvaapi paridhiraaneyu:   Multiply the diameter of a circle with 4 and keep it at different places and divide each with the odd numbers beginning from 3, 5, 7,...

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