What does alligation mean?
Alligation is a historical mathematical method used to solve problems involving mixtures. It answers questions such as: given ingredients of different prices or strengths, in what proportions should they be combined to yield a mixture with a specified average price or quality? The method came in two classical forms: 'alligation medial,' which finds the mean value of a known mixture, and 'alligation alternate,' which determines the quantities needed to reach a desired mean. Alligation was a staple of European commercial arithmetic from medieval times through the nineteenth century, taught to apothecaries, grocers, and merchants before algebraic techniques supplanted it. The word derives from the Latin alligare, meaning 'to bind to,' and its rare literal sense refers to the act of tying things together. Today it survives mostly in histories of mathematics and old textbooks, making it a charming relic of practical arithmetic.
A mathematical rule for finding the proportions in which substances of different prices or qualities must be mixed to produce a compound of a required price or quality.
"The textbook devoted a full chapter to alligation and its use in trade calculations."
Chiefly historical; encountered in older arithmetic texts and histories of mathematics.
The act of tying or binding things together.
"The surgeon described the ligation — or alligation, as older texts termed it — of the vessel with great precision."
Rare and largely obsolete in this literal sense.
The plural is uncommon, as alligation usually denotes a method rather than countable instances.
"Early printed arithmetics contain numerous worked examples of alligations of metals and spices."
Before algebra made it easy, merchants solved pricing puzzles with 'alligation' — a word so close to 'allegation' that even careful spellers do a double-take.
Reviewed by Deb Chak, Editor. AI-assisted content curated by RJS Tech Solutions LLP.
Etymology of alligation
Alligation comes from the Latin alligare, meaning 'to tie or bind to,' formed from ad- ('to') + ligare ('to bind'). The word entered English in the mid-sixteenth century, borrowed through late Latin usage. Its application to mixture problems reflects the notion of 'binding together' ingredients of different values into one blend. It shares its root with words such as 'ligature' and 'ligation,' and is unrelated in meaning to 'allegation,' despite the visual similarity that often causes confusion between them.
How alligation is actually used
Alligation is now chiefly historical or technical, appearing mainly in discussions of early modern arithmetic education and old commercial practice. It carries a formal, scholarly register. The spelling is easily confused with 'allegation,' so care is needed in writing.
Easily confused with alligation
An allegation is an unproven claim or accusation, whereas alligation is a mathematical method for computing mixtures — the two words share Latin roots but have entirely different meanings.