Proposition XI.7 — If two straight lines be parallel, and points be taken at ra…

Proof

Two parallel lines determine a plane (XI.2 extended). Any joining segment between points on the two parallels lies in this plane by XI.1.

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Depends on (2)

XI.1Proposition XI.1A part of a straight line cannot be in the plane of reference and a part in a plane more elevated.
XI.2Proposition XI.2If two straight lines cut one another, they are in one plane, and every triangle is in one plane.

Required by (dependents) (1)

XI.8Proposition XI.8If two straight lines be parallel, and one of them be at right angles to any plane, the remaining one will also be at…

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