Where does “cross-multiply” come from?

cross-multiply (English) comes from English multiply, from English ply, from English apply, from Middle English aplien, from Old French applier, from Latin applicō, from Latin ad-, from Latin īn- — in.

cross-multiply (English): To set the product of the extremes of a proportion equal to the product of its means

Definitions

  1. To set the product of the extremes of a proportion equal to the product of its means

Ancestry of “cross-multiply”, step by step

cross-multiply traces back through two separate lines of ancestry.

via English multiply

StepLanguageWordMeaning
1EnglishmultiplyTo increase the amount, degree or number of; To...
2EnglishplyA layer of material; A strand that, twisted...
3EnglishapplyTo lay or place; to put; To put to use; to use or...
4Middle Englishaplien
5Old Frenchapplierto bend; to apply
6Latinapplicōto apply
7Latinad-to; usually prefixed to verbs, in which cases it...
8Latinīn-un-, non-, not
9Latinînin, at, on, upon, from (space)
10Latinenlookǃ beholdǃ; reallyǃ?; come onǃ
11Proto-Italicenin
12Proto-Indo-Europeanh₁énin

via English cross

StepLanguageWordMeaning
1EnglishcrossA geometrical figure consisting of two straight...
2Frenchcroixcross; a representation of a cross; the cross as...
3GermanKreuzcross; clubs; sharp
4SpanishCruzcross
5Portuguesecruzcross
6Italiancrocecross
7Latincruxwooden frame on which criminals were crucified,...
8Proto-Italic*kruks
9Proto-Indo-Europeansḱer-to caw, crow
Every word from Proto-Indo-European h₁én