quadrare

Forms

quadrare (first-person singular present quàdro, first-person singular past historic quadrài, past participle quadràto, auxiliary (transitive or intransitive) avére or (alternatively when transitive) èssere)^[1]

Etymology

It is borrowed from Latin quadrāre (“to make square; to be square, to fit”), a verb formed from quadrus (“square”).^[2][3][4][5] Zingarelli and Battaglia's dictionary call it a learned word, while Wiktionary also allows that it was formed from Italian quadr- + -are, beside quadro.^[6][7][1] The Latin verb already had the extended and figurative uses “to suit, to fit”.^[8][9]

The Latin verb lives on in the western Romance languages: French carrer, Old Occitan cairar, Spanish cuadrar and Portuguese quadrar.^[10][9] Latin quadrus goes back to the root of quattuor (“four”), as in quārtus (“fourth”); as an adjective it is recorded only in Late Latin, but its feminine and neuter forms were classical nouns.^[1]

Earliest recorded meaning

Dante uses the verb in the Convivio (1304–1308) for the geometrical problem of squaring the circle: Lo cerchio per lo suo arco è impossibile a quadrare perfettamente (“because of its arc the circle cannot be squared perfectly”).^[2][11] Cortelazzo and Zolli give the sense of this first record as “to make square”.^[2] Zingarelli dates the word to about 1261.^[6]

Semantic evolution

The mathematical uses came first: Paolo dell'Abbaco, before 1374, used quadrare for working out the area of a plane figure, and Alessandro Piccolomini in 1561 for raising a number to the second power.^[2][11] The intransitive senses grew from the idea of exact correspondence: “to agree, to correspond” is recorded before 1510 in Sabadino degli Arienti, and “to tally”, of figures and accounts, in 1598.^[2] In Machiavelli's Mandragola (1518) the verb already means “to please, to suit someone”, and Berni has it for “to satisfy” before 1531.^[2][9]

The figurative quadrare la testa (or il cervello) a qualcuno, “to teach someone to think straight”, is recorded by Tommaseo and is still in the modern dictionaries.^[12][4][8] Today the commonest uses are in book-keeping and in the negative: i conti non quadrano, “the figures don't add up”, and qualcosa non mi quadra, “something doesn't convince me”.^[13][8]

Timeline

• About 1261 – Zingarelli's date for the first record.^[6]
• 1304–1308 – Dante uses quadrare of squaring the circle in the Convivio.^[2][11]
• Before 1374 – Paolo dell'Abbaco uses it for calculating an area.^[2]
• Before 1510 – Sabadino degli Arienti uses it for “to correspond, agree”.^[2]
• 1518 – In Machiavelli's Mandragola it means “to please, suit”.^[2]
• 1561 – Alessandro Piccolomini uses it for raising a number to the square.^[2]
• 1598 – P. Duodo uses it intransitively of figures that tally.^[2]

Meanings

Verb

1. (transitive) To square, to give something a square shape: quadrare una tavoletta di legno.^[4][13][5]
2. (transitive, geometry) To construct a square with the same area as a given figure; also, to calculate the area of an irregular figure.^[4][13][8]
3. (transitive, mathematics, uncommon) To raise a number to the second power.^[4][13][5]
4. (transitive, accounting) To check and balance the accounts, so that income and outgoings match.^[4][13][6]
5. (transitive, typography) To set the lines of a title or caption so that they have the same length.^[4][13][8]
6. (intransitive) Of figures or calculations, to be exact, to tally: il totale non quadra.^[4][13][5]
7. (intransitive) To correspond exactly, to match: le spese quadrano con gli incassi.^[4][13][6]
8. (intransitive, figurative) To fit, to be suitable; to make sense, to be convincing, especially in the negative: la sua versione dei fatti non mi quadra.^[4][13][8]
9. (intransitive, colloquial) To please, to suit someone: questo piano non mi quadra.^[4][13][5]

Word family

• quadrato
• quadratura
• quadrabile
• riquadrare
• squadrare
• quadramento
• quadratore

Related words

• quadro
• quadrettato
• squadra
• Latin quadrus
• Latin quadrō

Usage notes

In the intransitive senses the auxiliary is avere or essere, but the compound tenses are rare.^[8][13] Battaglia's dictionary lists an old, separate quadrare “to come fourth, to make up a group of four”, formed from quadro in the sense of “a fourth”, with examples from the Cortona lauds and Sacchetti.^[14]

References

1. ^ a b c d Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h i j k l Cortelazzo, Manlio; Zolli, Paolo (1999), Dizionario etimologico della lingua italiana, 2nd ed. by Manlio Cortelazzo and Michele A. Cortelazzo, Bologna: Zanichelli
3. ^ Nocentini, Alberto; Parenti, Alessandro (2010), l'Etimologico: vocabolario della lingua italiana, Firenze: Le Monnier
4. ^ a b c d e f g h i j k De Mauro, Tullio (ed.) (2003), Grande dizionario italiano dell'uso, CD-ROM version 2.0, Torino: UTET
5. ^ a b c d e Sabatini, Francesco; Coletti, Vittorio; Manfredini, Manuela (2026), Dizionario italiano Sabatini Coletti, digital ed., Milano: Sansoni / Rizzoli Larousse
6. ^ a b c d e Zingarelli, Nicola (2009), Lo Zingarelli 2010: vocabolario della lingua italiana, Bologna: Zanichelli
7. ^ Battaglia, Salvatore; Bàrberi Squarotti, Giorgio (1961–2002), Grande dizionario della lingua italiana, 21 vols., Torino: UTET; digital ed. Accademia della Crusca
8. ^ a b c d e f g Duro, Aldo (ed.) (1986–1994), Vocabolario della lingua italiana, Roma: Istituto della Enciclopedia Italiana; online ed. treccani.it/vocabolario (2008 copy)
9. ^ a b c Battisti, Carlo; Alessio, Giovanni (1950–1957), Dizionario etimologico italiano, 5 vols., Firenze: Barbèra (reprint 1975)
10. ^ Meyer-Lübke, Wilhelm (1935), Romanisches etymologisches Wörterbuch, 3rd ed., Heidelberg: Winter
11. ^ a b c Battaglia, Salvatore; Bàrberi Squarotti, Giorgio (1961–2002), Grande dizionario della lingua italiana, 21 vols., Torino: UTET; digital ed. Accademia della Crusca, p. 15, 11
12. ^ Tommaseo, Niccolò; Bellini, Bernardo (1861–1879), Dizionario della lingua italiana, 4 vols., Torino: UTET
13. ^ a b c d e f g h i j k Devoto, Giacomo; Oli, Gian Carlo; Serianni, Luca; Trifone, Maurizio (2026), Nuovo Devoto–Oli: il vocabolario dell'italiano contemporaneo, digital ed., Milano: Le Monnier
14. ^ Battaglia, Salvatore; Bàrberi Squarotti, Giorgio (1961–2002), Grande dizionario della lingua italiana, 21 vols., Torino: UTET; digital ed. Accademia della Crusca, p. 15, 12