Commentary on Proposition I.33¶
Back to Proposition I.33.
This proposition is, as Proclus says (p. 385, 5), the connecting link between the exposition of the theory of parallels and the investigation of parallelograms. For, while it only speaks of equal and parallel straight lines connecting those ends of equal and parallel straight lines which are in the same directions, it gives, without expressing the fact, the construction or origin of the parallelogram, so that in the next proposition Euclid is able to speak of “parallelogrammic areas” without any further explanation.