- The name sine came to us from the Latin sinus, a term related to a curve, fold, or hollow. It is often interpreted as the fold of a garment, which was used as we would use a pocket today. The use in mathematics probably comes about through the incorrect translation of a Sanskrit word. Here is a brief description of how that came about from Passage to China by Amartya Sen. “In his Sanksrit mathematical treatise completed in 499 AD, Aryabhata used jya-ardha (Sankscrit for “chord half”), shortened later into jya, for what we now call “sine.” Arab mathematicians in the eighth century transliterated the Sanskrit word jya into the proximate sound of jiba and then later changed it into jaib (with the same consonants as jiba), which is a good Arabic word, meaning a bay or a cove, and it was this word that was later translated by Gherardo of Cremona (circa 1150) into its equivalent Latin word for a bay or a cove, viz., sinus, from which the modern term “sine” is derived.”
- When Leonardo de Fibonacci used the term in his writing, it became permanent. According to Carl Boyar’s “A History of Mathematics”, the idea of the sine of an angle came from an Indian book written around the year 400. The early use of sine referred to a length of the chord in a circle. It was not until the 1700’s and Leonid Euler [pronounced Oiler] that it became common to use the sine as a ratio.
- The long road to the long word correlation, begins with the ancient Sanskrit word for scales, tula. The action of a scale to lift or support the weight led to the Greek word telamon for one who supports or bears something. This flows into the Latin word latus for to carry. The re prefix for back gives us relate, literally to carry back. Finally the co is added to indicate something the same or shared. Two things are correlated if there is some common thing back to which we can carry them both.
- The first use of the term in the true statistical sense is attributed to Francis Galton. In The History of Statistics by Stephen Stigler, he writes, “In December 1888,… Galton read a short paper to the Royal Society, ‘Co-relations and their measurement, chiefly from anthropometric data’.” In it was the first use of what he called his “index of co-relation.” Stigler also explains, “The initial spelling of the term co-relation seems to have been a conscious attempt on Galton’s part to distinguish his term from the word correlation, which was already in common use. In particular, the physicist W. R. Grove had published The Correlation of Physical Forces in 1846, …. Grove wrote that two correlated ideas would be ‘inseperable, even in mental conception,” but he emphasized …. ‘one …. cannot take place without involving the other’.”
The term “geometric” was first used by the pythagoreans according to Iamblichus ON NICHOMACHUS’S *INTRODUCTION TO ARITHMETIC*”
- In ancient days in the time of Pythagoras & the mathematicians of his school there were only three means (mesotetes) the arithmetic, the geometric (gometrike) , and a third in order which was then called subcontrary…renamed harmonic.
Archytas cited by Porphyry:
- Now there are 3 means in music: 1st the arithmetic (the first exceeds the second by the same amount that the second exceeds the third; 2nd the geometric (gametrika) (the first term is to the second as the second is to the third); and 3rdly the subcontrary, the so-called harmonic (whaterver part of itself the first term exceeds the second, the middle term exceeds the third by the same part of the third.