skey-d-tro-
“splitting tool, thing that divides”scissors, schism, schizophrenia
Instrumental of *skey-d- giving Greek skhizein, English scissors, schism, schizophrenia.
Discussion
The PIE form *skey-d-tro- (splitting tool, thing that divides) derives from the root *skey- (to cut, to split, to separate) with the instrumental suffix *-tro- producing a noun of instrument — literally "the thing that cuts/splits." This is the ancestral form behind one of the most recognisable cognate sets in European languages: the word for scissors.
Latin scindere (to cut, to split, to tear) continues the verbal root directly and generated: scissors (via Medieval Latin cisōria, cutting instruments, influenced by the root), schism (from Greek skhísma, a split), rescind (to cut back, to annul), and abscission (cutting away). The past participle scissus (cut) is transparent in these derivatives.
Greek skhízein (σχίζειν, "to split, to cleave") provides the Hellenic reflex with the expected Greek treatment of the initial cluster. The derivatives are medically and scientifically prominent: schizophrenia (literally "split mind," coined 1908 by Eugen Bleuler), schist (a rock that splits into layers), and schistosomiasis (infection by the split-bodied fluke worm). The combining form schizo- has become productive in modern English well beyond its Greek origin.
The Germanic branch shows the root in Old English scītan (to separate, to divide — the ancestor of a modern English word whose vulgar sense developed from the original meaning of bodily separation/excretion) and more transparently in shed (to separate, to cast off, from OE scēadan "to divide, to separate") and the dialectal shide (a thin piece of split wood). The watershed (the ridge that divides/sheds water into different drainage basins) preserves the "divide" sense clearly.
Old Irish scían (knife, the cutting/splitting tool) and Welsh ysgain (light, thin — that which has been split/pared down) provide Celtic attestation.
The suffix *-tro- is the same instrumental suffix found in *h₂erh₃-tro- (plough, the thing that ploughs) and other PIE tool-words. The pattern ROOT + *-tro- = TOOL is one of PIE's most regular derivational processes, and its survival in Latin -trum (aratrum, plough; claustrum, lock; rostrum, beak/prow) and Greek -tron (ἄροτρον, plough; λέκτρον, bed) confirms its productivity.
The semantic field of *skey- — cutting, splitting, dividing, separating — intersects with *ḱrey- (to sieve, to separate, to judge) at the point of "separation," but the two roots are phonologically and semantically distinct: *skey- emphasises physical cutting, while *ḱrey- emphasises cognitive/perceptual discrimination. Together they show that PIE had a rich vocabulary for different modes of division.