Etymology
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plan (n.)

1670s as a technical term in perspective drawing; more generally by 1706 as "the representation of anything drawn on a plane; a drawing, sketch, or diagram of any object," from French plan "ground plot of a building, map," literally "plane surface" (mid-16c.), from Latin planum "level or flat surface," noun use of adjective planus "level, flat" (from PIE root *pele- (2) "flat; to spread").

The notion is of "a drawing on a flat surface." A doublet of plain via a later, learned French form. The meaning "scheme of action, formulated scheme for the accomplishment of some object or attainment of an end" is by 1713.

plan (v.)

1728, "make a plan of; put on paper the parts, dimensions, and methods of construction of," from plan (n.). By 1737 as "to scheme, to devise ways and means for (the doing of something)." Related: Planned; planning; plans. Planned economy is attested by 1931. Planned Parenthood (1942) formerly was Birth Control Federation of America.

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Definitions of plan
1
plan (v.)
have the will and intention to carry out some action;
He plans to be in graduate school next year
The rebels had planned turmoil and confusion
Synonyms: be after
plan (v.)
make plans for something;
He is planning a trip with his family
plan (v.)
make or work out a plan for; devise;
plan an attack
Synonyms: project / contrive / design
plan (v.)
make a design of; plan out in systematic, often graphic form;
plan the new wing of the museum
Synonyms: design
2
plan (n.)
a series of steps to be carried out or goals to be accomplished;
they drew up a six-step plan
they discussed plans for a new bond issue
Synonyms: program / programme
plan (n.)
an arrangement scheme;
a plan for seating guests
Synonyms: design
plan (n.)
scale drawing of a structure;
the plans for City Hall were on file
Synonyms: architectural plan
From wordnet.princeton.edu