Newton's (1660 AD) Power Series

nihatya chapavargena chapam tatthathphalani cha haret

samulayugvargaistrijyavargahatai: kramaat chapam phlani

chadhodhonyasyoparyupari tyajet jivaptyai,

sangraho syaiva vidvan-ityadina krtha:

nihathya chapavargena rupam tattatphalani cha hared vimulayugvargaistrijyavargahatai:

kramat kintu vyasadalenaiva dvighnenadyam vibhajyataam phalanyadhodha:

kramaso nyasyoparyupari tyajet saraptyai, sangraho asyaiva stenastri-tyadinaa krta:

Multiply repeatedly the arc by its square and divide by the square of even numbers increased by that number and then multiplied by the square of radius. Place the arc and result one below the other and subtract each from what is above it. To derive the arc, which are collected, beginning with the expression Vidvan (katapayadi number). Multiply repeatedly, the unit measurement which is the radius, by the square of the arc and divide by the square of even numbers decreased by that number and then multiplied by the square of radius; the first is, however, to be divided by twice the radius. Place the results one below the other and subtract each from the one above it. That is the method to derive the saras, which are collected in the beginning with stena. (This equation is now known as Newton power series.)]]>

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