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PROPOSITION 1.

A part of a straight line cannot be in the plane of reference and a part in a plane more elevated.

For, if possible, let a part AB of the straight line ABC be in the plane of reference, and a part BC in a plane more elevated.

There will then be in the plane of reference some straight line continuous with AB in a straight line.

Let it be BD; therefore AB is a common segment of the two straight lines ABC, ABD: which is impossible, inasmuch as, if we describe a circle with centre B and distance AB, the diameters will cut off unequal circumferences of the circle.

Therefore a part of a straight line cannot be in the plane of reference, and a part in a plane more elevated. Q. E. D. 1 2

1 1. the plane of reference, τὸ ὑποκείμενον ἐπίπεδον, the plane laid down or assumed.

2 2. more elevated, μετεωροτέρῳ.

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