Why do we say this?

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WHY DO WE SAY THIS?

sinus
chorda

1. WHERE DID THE WORD COME FROM?
   “SINUS”

The word “sine” is of Latin origin. If we look in the Latin-Russian dictionary, we see the following meanings of this word: 1) curvature, curvature, bending, convexity; 2) loose, pocket, fold of that (ancient Roman clothing) on ​​the chest; 3) dress, clothing; 4) breasts, hugs; 5) tender love, care;

6. middle, center; 7) refuge, shelter; 8) bay, bay; 9) vladina, deepening, failure. The word “sinus” is well known in the meaning of “sinus”, “cavity”. However, none of these many meanings have anything to do with sine in trigonometry. Where did this term come from?

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Trigonometry first appeared in the 1st-2nd centuries AD in Alexandria, in the works of famous Alexandrian astronomers, the largest of whom was Claudius Ptolemy. However, in Ptolemy’s trigonometry the main concept was not the sine, but the chord. In Ptolemy’s book “Mathematical System” there were tables of the dependence of the lengths of chords on the lengths of the subtended immidus, and the arcs were measured in degrees, minutes and seconds, and the chords - in parts of the radius: here the radius was considered equal to 60 parts, the chords were measured in these fractions of the radius, in their “minutes” (60th shares) and in their “seconds” (60th shares of “minutes”). This “six-desateric” division of arcs and chords was taken up by the Alexandrian astronomers from the Babylonians.

The word “chord” comes from the Greek word “horde” - “intestine”, “string” (in ancient Greece, strings were extracted from ox intestines). Both in Ancient Greece and in the Alexandrian school this word was not associated with the chord. Both Euclid, Ptolemy, and other Alexandrian scholars call a chord “straight in a circle,” meaning a straight segment inscribed in a circle (they also call a triangle inscribed in a circle “triangle in a circle”).

In the 5th century AD The Alexandrian scientific school was destroyed by Christian fanatics, led by “Saint” Cyril. At this time, one of the Alexandrian language astronomers, named Paulos, fled to India, where he wrote an account of the achievements of the Alexandrian astronomers in Sanskrit, the scientific language of the Indians. This book was given the name “Paulisa-siddhanta” by the Indians - “The Teachings of Paulisa,” as the Indians called Paulos. In this book, the chord was called by the Sanskrit word “jiva”, which also denoted the string of a bow, the arc - by the same word as the bow, and the height of the segment bounded by the arc and the chord contracted by it - by the same word as the arrow.

Later Indian astronomers and mathematicians, the largest of whom was Brahmagupta, who worked in the 7th century, replaced chords with half lines, that is, sine lines. They first called these lines “ard-jiva” - “half-string”, and then for brevity they began to call them simply “jiva”.

In the 8th century, one of the “siddhantas” of Indian scholars was translated into Arabic under the name “Sindhint” (a distortion of the word “siddhanta” was influenced by the Arabic name for India “Hind”). In this book, the words “jiva”, which no longer denoted a chord, but a line of sine, were written in Arabic letters. But, since the Arabs do not have the sound “v”, but only “b” and a short “u”, translators into Arabic wrote not “jiva”, but “jiba”. But in Arabic, only long vowels are indicated, and short vowels are omitted, and the long “i” is indicated by the same letter as the semi-vowel “y”, while in the word “jiba” the sound “i” was long, and “a” was short. Therefore, the words “jiba” were written in Arabic exactly the same as the words “jaib”, and soon they began to pronounce it “jaib”. The word “jaib” means sinus, vladina, that is, what in Latin is the word “sinus”. Therefore, when in the 12th century Arabic astronomical and mathematical books began to be translated into Latin, the words “jaib”, which signifies the line of sine, were translated by the word “sinus”.

In those cases where the word “jiva” denoted a chord, the Arabs translated it with the word “batar”.

The word “batar”, which denoted not only a bowstring, but also a string, was translated into Latin by the word “chorda” - a transcription of the Greek word “chord” already known to us.

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2. WHERE CAME FROM
   MATHEMATICAL TERM
   “ROOT”

The word “root” is a Russian word, but the mathematical meaning of this word has a very long and interesting history.

Ancient Greek scientists - Pythogoreans (5th century BC) associated geometric concepts with numbers and depicted the product of two and three factors in the form of rectangles and rectangular parallelepipeds, the sides and edges of which are equal to som factors. Therefore, they call the product of two and three som factors of the corresponding “flat” and “solid” numbers, and the product of two and three equal som factors - “square” and “cubic” numbers, respectively. It is this terminology that is used in the varithmetic books of Euclid’s Elements (3rd century BC), a remnant of this terminology is our terms “square” and “cube” for numbers of the form $n^2$ and $n^3$.

According to Pythogorean terminology, the root of a “square” number is called “side” (in Greek “pleeura”), which also means “shell”, from which “pleeuritis” is an inflammation of the membrane of the lung, and “base” (in Greek “basis”), from which our word “base”.

When in the 5th century A.D. e. The Alexandrian scientific school perished, and the Alexandrian astronomer Paulos fled to India, the term “base” was translated into Sanskrit by the word “pada”, meaning base, as well as the root of a plant.

In the 8th century, when translating the “siddhantas” of Indian scholars into Arabic, the translator understood the words “pada” as “root” and translated it into the Arabic word “jizr”, denoting the root. In parallel, in Arabic mathematical literature there was another term for the root of a number - “dill” (“side” or “edge”), a translation of the Greek word “pleevra”: if the word “jizr” was used for square roots and roots of quadratic equations, then the word “dill” was used for roots of calculus powers: mathematicians writing in Arabic called the cube root “edge of the cube”, the root of the 4th degree - “edge” square-square”, the root of the 5th degree is “edge of a square-cube”, the root of the 6th degree is “edge of a cube-cube”, etc.

In the 12th century, when translating Arabic terms into Latin, the word “jizr” was translated by the word “radix”, also denoting a root (from this word, which also denoted a “root vegetable”, our word “radish” comes from), and the word “dill” was translated by the word “latus”, also denoting a side and a rib. In Magnitsky’s “Arithmetic” the word “radix” was left without translation - “radix”, and the word “latus” was translated by the word “side”, but later both of these terms were coined by the Russian translation of the word “radix” - the word “root”. However, sometimes the term “radical” is also used with this word, which also comes from the Latin term “radix”.

B. A. ROSENFELD