In by Mark Goodman

A sloping roof member that supports the roof covering which extends from the ridge or the hip of the roof to the eaves. A common rafter is one that runs square with the plate and extends to the ridge. A hip rafter extends from the outside angle of the plate toward the apex of the roof, and is 2 inches deeper or wider than a common rafter. A valley rafter extends from an inside angle of the plates toward the ridge of the house.

Merriam-Webster Online Dictionary
rafter (noun)
any of the parallel beams that support a roof
rafter (noun)
one who maneuvers logs into position and binds them into - rafts
one who travels by raft
rafter (Wikipedia)
Common rafters without collar beams form most of this roof. There is not always a ridge board or beam where the rafter tops meet. Under the midsections of the rafters are purlins which support the common rafters and are supported by principal rafters. This roof ends in an octagonal hip.
A double roof (using a Norman truss), common rafters supported by principal rafters (top chords in this case) and an unusual extra layer of common rafters on the lower half to form a gallerie. Note how the rafter poles for the gallerie tie-in. The Bequet-Ribault House was built c. 1793 near Ste. Geneviève, Missouri. It is one of five poteaux-en-terre buildings that survive in the US.
Rafter and tie-beam joints (Carpentry and Joinery, 1925)
Coyau or sprocket. Labeled A

A rafter is one of a series of sloped structural members that extend from the ridge or hip to the wall plate, downslope perimeter or eave, and that are designed to support the roof deck and its associated loads. A pair of rafters is called a couple. In home construction, rafters are normally made of wood. Exposed rafters are a feature of some traditional roof styles.

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