The etymology of math terms,
collected by S.K.Stephenson.

Calculus:

From Apple's Mac OS X Dictionary:

Latin, literally small pebble (as used on [a counting board style] abacus).

The Roman expression for to calculate is calculus ponere - literally, to place pebbles. When a Roman wished to settle accounts with someone, he would use the expression vocare aliquem ad calculosto call them to the pebbles. Which meant they would use a counting board style abacus.

Calculus is the name given by Gottfried Wilhelm Leibniz (1646 - 1716) to that branch of mathematics that studies change, and that includes the study of limits, derivatives, integrals, and infinite series.

Latus Rectum:

From http://bit.ly/LatusRectum:

latus rectum plural latera recta (noun): the Latin noun latus, stem later-, meant "side" or, in geometry, "chord"; the word is of unknown prior origin. The adjective rectum, which is related to English right, as in right angle, is the past participle of Latin regere "to lead in a straight line or in the right direction." The Indo-European root is reg- "to move in a straight line." In analytic geometry, the latus rectum is the chord of a conic section that passes through the focus and makes a right angle with the axis of the conic.

Sine:

From American Heritage Talking Dictionary, Copyright © 1997 The Learning Company, Inc.:

Medieval Latin sinus (mistranslation of Arabic jayb, sine, as if jayb, fold in a garment), from Latin, curve, fold.

From http://aleph0.clarku.edu/~djoyce/java/trig/sines.html on 4/25/2003:

The Sanskrit word for chord-half was jya-ardha, which was sometimes shortened to jiva. This was brought into Arabic as jiba, and written in Arabic simply with two consonants jb, vowels not being written. Later, Latin translators selected the word sinus to translate jb thinking that the word was an arabic word jaib, which meant breast, and sinus had breast and bay as two of its meanings. In English, sinus was imported as "sine".

This word history for "sine" is interesting because it follows the path of trigonometry from India, through the Arabic language from Baghdad through Spain, into western Europe in the Latin language, and then to modern languages such as English."

From http://campus.northpark.edu/math/PreCalculus/Transcendental/Trigonometric/Definition/ on 8/26/2006

... the story behind the name "sine" is the most interesting. It comes from a series of mistranslations of the Indian word jya for "chord", which refers to any line segment whose endpoints lie on a circle. The first partial tables for the sine function were computed in around 500 AD by Aryabhata as half the length of the chord CS in the following picture:

as the angle t varied. The Indian phrase jya-ardha = "chord-half" for this function was abbreviated simply to jya. However, around 700 AD this term was transliterated into the meaningless Arabic word jiba. Unfortunately, this led European scholars, who were trying to translate the works of Arabic mathematicians, such as Abu'l-Wafa, to mistake jiba for the word jaib, meaning "fold". Around 1000 AD, European mathematicians such as, Fibonacci, then translated jaib into the equivalent Latin word sinus, meaning "fold", "hollow", or "cavity", from which we get the name "sine"!