Etymology
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Words related to *sek-

bisect (v.)
"to cut in two," 1640s, from Modern Latin bisectus, from Latin bi- "two" (see bi-) + secare "to cut" (from PIE root *sek- "to cut"). Related: Bisected; bisecting.
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dissect (v.)

c. 1600, "cut in pieces," from Latin dissectus, past participle of dissecare"cut in pieces," from dis- "apart" (see dis-) + secare "to cut" (from PIE root *sek- "to cut"). Or perhaps a back-formation from dissection. Specifically as "separate the distinct parts of an animal or plant for the purpose of studying its organization and functions or its morbid affections" from 1610s. Transferred sense of "examine part by part or point by point" is from 1630s. Related: Dissected; dissecting.

hacksaw (n.)
1867, from hack (v.1) + saw (n.1) "toothed cutting tool."
insect (n.)

c. 1600, from Latin (animal) insectum "(animal) with a notched or divided body," literally "cut into," noun use of neuter past participle of insectare "to cut into, to cut up," from in- "into" (from PIE root *en "in") + secare "to cut" (from PIE root *sek- "to cut"). The Latin word is Pliny's loan-translation of Greek entomon "insect" (see entomology), which was Aristotle's term for this class of life, in reference to their "notched" bodies.

First in English in 1601 in Holland's translation of Pliny. In zoology, in reference to a class of animals, 1753. Translations of Aristotle's term also form the usual word for "insect" in Welsh (trychfil, from trychu "cut" + mil "animal"), Serbo-Croatian (zareznik, from rezati "cut"), Russian (nasekomoe, from sekat "cut"), etc. Insectarian "one who eats insects" is attested from 1893.

Among the adjectival forms that have been tried in English (and mostly rejected by disuse) are insectile (1620s), insectic (1767), insective (1834), insectual (1849), insectine (1853), insecty (1859), insectan (1888).

It is curious that in the eyes of the Anglo-Saxon naturalists, the frog, the toad, the lizard or eft (efte), and other reptiles, were usually placed under the head of insects ; and this odd classification was preserved to rather a late period. [Thomas Wright, "Anglo-Saxon and Old English Vocabularies," 1884]
intersect (v.)
1610s (trans.), back-formation from intersection, or else from Latin intersectus, past participle of intersecare "intersect, cut asunder," from inter "between" (see inter-) + secare "to cut" (from PIE root *sek- "to cut"). Intransitive sense is from 1847. Related: Intersected; intersecting.
resect (v.)

"cut off or away, pare off," 1650s, from Latin resectus, past participle of resecare "to cut off, cut loose, curtail," from re-, here perhaps an intensive prefix (see re-), + secare "to cut" (from PIE root *sek- "to cut"). The surgical sense of "excising of some part," of a bone, etc., (1846) seems to be the sole surviving one. Related: Resected; resecting.

saw (n.1)

[toothed cutting tool] Middle English saue, from Old English sagu, from Proto-Germanic *sago "a cutting tool" (source also of Old English seax "knife," Old Norse sög, Norwegian sag, Danish sav, Swedish såg, Middle Dutch saghe, Dutch zaag, Old High German saga, German Säge "saw"), from PIE root *sek- "to cut" (source also of Latin secare "to cut").

In reference to its use as a musical instrument, by 1905. Saw-grass, the long, toothed grass found in the Southern U.S., is attested by 1822. The saw-fly (1773), destructive to plants, is so called for the construction of the insect's egg-depositing organ.

Saxon (n.)

c. 1200, Sexun, Saxun, "member of a people or tribe formerly living in northern Germania who invaded and settled in Britain 5c.-6c.," from Late Latin Saxonem (nominative Saxo; also source of Old French saisoigne, French Saxon, Spanish Sajon, Italian Sassone), usually found in plural Saxones, probably from a West Germanic tribal name (represented by Old English Seaxe, Old High German Sahsun, German Sachse "Saxon").

This is traditionally regarded as meaning "warrior with knives" (compare Middle English sax, Old English seax, Old Frisian, Old Norse sax "knife, short sword, dagger," Old High German Saxnot, name of a war-god), from Proto-Germanic *sahsa- "knife," from PIE root *sek- "to cut." But Watkins considers this doubtful.

The word figures in the oft-told tale, related by Geoffrey of Monmouth, who got it from Nennius, of the treacherous slaughter by the Anglo-Saxons of their British hosts:

Accordingly they all met at the time and place appointed, and began to treat of peace; and when a fit opportunity offered for executing his villany, Hengist cried out, "Nemet oure Saxas," and the same instant seized Vortigern, and held him by his cloak. The Saxons, upon the signal given, drew their daggers, and falling upon the princes, who little suspected any such design, assassinated them to the number of four hundred and sixty barons and consuls ....

The OED editors helpfully point out that the murderous shout in correct Old English (with an uninflected plural) would be nimað eowre seax. For other Germanic national names that may have derived from characteristic tribal weapons, see Frank, Lombard. Celtic languages used their form of the word to mean "an Englishman, one of the English race" or English-speaking person in Celtic lands (for example Welsh Sais, plural Seison "an Englishman;" Seisoneg "English;" compare Sassenach).

As an adjective from late 14c. (earlier was Saxish, c. 1200); in reference to the later German state of Saxony (German Sachsen, French Saxe) in central Germany it is attested by mid-14c. Bede distinguished the Anglo-Saxons, who conquered much of southern Britain, from the Ealdesaxe "Old Saxons," who stayed in Germany.

Saxon is the source of the -sex in Essex, Sussex, etc. (compare Middlesex, from Old English Middel-Seaxe "Middle Saxons").

scythe (n.)

"long, curving blade made fast to a handle, convenient for swinging, and used in mowing or reaping," Middle English sithe, sythe, from Old English siðe, sigði, from Proto-Germanic *segitho "sickle" (source also of Middle Low German segede, Middle Dutch sichte, Old High German segensa, German Sense), from PIE root *sek- "to cut."

The sc- spelling began by early 15c. (earliest surviving use of it is in an English word in a document written in Latin), from influence of Latin scissor "carver, cutter" and scindere "to cut." Compare French scier "saw," a false spelling from sier. Since the Middle Ages, it was carried by personifications of Time and Death.

secant (n.)

one of the fundamental functions of trigonometry, 1590s, from Latin secantem (nominative secans) "a cutting," present participle of secare "to cut" (from PIE root *sek- "to cut"). First used by Danish mathematician Thomas Fincke in "Geometria Rotundi" (1583). Related: Secancy ("state of being a secant").