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THe common section of two Places is a streight Line.
If Two Planes AB, CD, cut one another, their common section EF shall be a streight Line. For if it were not, take Two Points common to both Planes which let be E and F; and draw a
strait Line from the point E to the point F, in the Plane AB, which let be EHF. Draw also in the Plane CD a streight Line from E to F; if it be not the same with the former, let it be EGF.
Demonstration. Those Lines drawn in the Two Planes are two different Lines, and they comprehend a space; whch is contrary to the Twelfth Maxim. Thence they are but one Line, which being in both Planes, shall be their common section.
THis Proposition is fundamental. We do suppose it in Gnomonicks, when we represent in a Dial, the Circles of the hours, marking only the common section of their Planes, and that of the Wall.