Etymology
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periphery (n.)

late 14c., periferie, "atmosphere around the earth," from Old French periferie (Modern French périphérie) and directly from Medieval Latin periferia, from Late Latin peripheria, from Greek peripheria "circumference, outer surface, line round a circular body," literally "a carrying around," from peripheres "rounded, moving round, revolving," peripherein "carry or move round," from peri "round about" (see peri-) + pherein "to carry," from PIE root *bher- (1) "to carry."

In geometry, the meaning "outside boundary of a closed figure," especially the circumference of a circle, is attested in English from 1570s; the general sense of "boundary, surface" is from 1660s.

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diagram (n.)

1610s, "an illustrative figure giving only the outlines or general scheme of the object;" 1640s in geometry, "a drawing for the purpose of demonstrating the properties of a figure;" from French diagramme, from Latin diagramma "a scale, a musical scale," from Greek diagramma "geometric figure, that which is marked out by lines," from diagraphein "mark out by lines, delineate," from dia "across, through" (see dia-) + graphein "write, mark, draw" (see -graphy). Related: Diagrammatic; diagrammatically.

The verb, "to draw or put in the form of a diagram," is by 1822, from the noun. Related: Diagrammed; diagramming.

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affinity (n.)
c. 1300, "relation by marriage" (as opposed to consanguinity), from Old French afinite "relationship, kinship; neighborhood, vicinity" (12c., Modern French affinité), from Latin affinitatem (nominative affinitas) "relationship by marriage; neighborhood," noun of state from affinis "adjoining, adjacent," also "kin by marriage," literally "bordering on," from ad "to" (see ad-) + finis "a border, a boundary" (see finish (v.)).

Spelling was re-Latinized in early Modern English. Used figuratively in English since c. 1600 of structural relationships in chemistry, philology, geometry, etc. Meaning "natural liking or attraction, a relationship as close as family between persons not related by blood" is from 1610s.
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rectangle (n.)

in geometry, "quadrilateral plane figure having all its angles right and all its opposite sides equal," 1570s, from French rectangle (16c.), from rect-, combining form of Latin rectus "right" (from PIE root *reg- "move in a straight line," with derivatives meaning "to direct in a straight line") + Old French angle (see angle (n.)). Late/Medieval Latin rectiangulum meant "a triangle having a right angle," noun use of neuter of rectiangulus "having a right angle." When the adjacent sides are equal, it is a square, but rectangle usually is limited to figures where adjacent sides are unequal.

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obtuse (adj.)

early 15c., "dull, blunted, not sharp," from Latin obtusus "blunted, dull," also used figuratively, past participle of obtundere "to beat against, make dull," from ob "in front of; against" (see ob-) + tundere "to beat," from PIE *(s)tud-e- "to beat, strike, push, thrust," from root *(s)teu- "to push, stick, knock, beat" (source also of Latin tudes "hammer," Sanskrit tudati "he thrusts"). Sense of "stupid, not acutely sensitive or perceptive" is by c. 1500. In geometry, in reference to a plane angle greater than a right angle," 1560s. Related: Obtusely; obtuseness.

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prism (n.)

1560s, in geometry, "a solid whose bases or ends are any similar, equal, and parallel plane polygons, and whose sides are parallelograms" (not always triangular), from Late Latin prisma, from Greek prisma "a geometrical prism, trilateral column," (Euclid), literally "something sawed (as a block of wood), sawdust," from prizein, priein "to saw" (related to prion "a saw"), which is of uncertain origin. Euclid chose the word, apparently, on the image of a column with the sides sawn off.

Specific sense in optics, "an instrument (usually triangular) with well-polished sides of glass, quartz, etc., which refracts light and spreads it in a spectrum," is attested from 1610s.

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parallel (adj.)

1540s, in geometry, of lines, "lying in the same plane but never meeting in either direction;" of planes, "never meeting, however far extended;" from French parallèle (16c.) and directly from Latin parallelus, from Greek parallēlos "parallel," from para allēlois "beside one another," from para- "beside" (see para- (1)) + allēlois "each other," from allos "other" (from PIE root *al- "beyond"). Figurative sense of "having the same direction, tendency, or course" is from c. 1600.

As a noun from 1550s, "a line parallel to another line." Meanings "a comparison made by placing things side by side" and "thing equal to or resembling another in all particulars" are from 1590s.  Parallel bars as gymnastics apparatus is recorded from 1868.

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problem (n.)

late 14c., probleme, "a difficult question proposed for discussion or solution; a riddle; a scientific topic for investigation," from Old French problème (14c.) and directly from Latin problema, from Greek problēma "a task, that which is proposed, a question;" also "anything projecting, headland, promontory; fence, barrier;" also "a problem in geometry," literally "thing put forward," from proballein "propose," from pro "forward" (from PIE root *per- (1) "forward") + ballein "to throw" (from PIE root *gwele- "to throw, reach").

The meaning "a difficulty" is mid-15c. Mathematical sense of "proposition requiring some operation to be performed" is from 1560s in English. Problem child, one in which problems of a personal or social character are manifested, is recorded by 1916. Phrase _______ problem in reference to a persistent and seemingly insoluble difficulty is attested from at least 1882, in Jewish problem. Response no problem "that is acceptable; that can be done without difficulty" is recorded from 1968.

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fractal (n.)

"never-ending pattern," 1975, from French fractal, ultimately from Latin fractus "interrupted, irregular," literally "broken," past participle of frangere "to break" (from PIE root *bhreg- "to break"). Coined by French mathematician Benoit Mandelbrot (1924-2010) in "Les Objets Fractals."

Many important spatial patterns of Nature are either irregular or fragmented to such an extreme degree that ... classical geometry ... is hardly of any help in describing their form. ... I hope to show that it is possible in many cases to remedy this absence of geometric representation by using a family of shapes I propose to call fractals — or fractal sets. [Mandelbrot, "Fractals," 1977]

The term was suggested earlier in Mandelbrot's 1967 book, "How Long is the Coast of Britain -- Statistical Self-Similarity and Fractional Dimension."

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liberal arts (n.)

late 14c., translating Latin artes liberales; the name for the seven attainments directed to intellectual enlargement, rather than immediate practical purpose, and thus deemed worthy of a free man (liberal in this sense is opposed to servile or mechanical). They were divided into the trivium — grammar, logic, rhetoric (see trivial) — and the quadrivium — arithmetic, geometry, music, astronomy. Explained by Fowler (1926) as "the education designed for a gentleman (Latin liber a free man) & ... opposed on the one hand to technical or professional or any special training, & on the other to education that stops short before manhood is reached."

The study of [the classics] is fitly called a liberal education, because it emancipates the mind from every narrow provincialism, whether of egoism or tradition, and is the apprenticeship that every one must serve before becoming a free brother of the guild which passes the torch of life from age to age. [James Russell Lowell, "Among my Books"]
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