Page:Euclid's Elements 1714 Barrow translation.djvu/18

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XXXVI. In a Parallelogram ABCD, when a diameter AC, and two lines EF, HI parallel to the ides, cutting the diameter in one and the ame point G, are drawn, o that the Parallelogram be divided by them into four parallelograms; thoe two DG, GB, through which the diameter paeth not, are called Complements; and the other two HE, FI, through which the diameter paeth, the Parallelograms tanding about the diameter.

A Problem is, when omething is propoed to be done or effected.

A Theoreme is, when omething is propoed to be demontrated.

A Corollary is a conectary, or ome conequent truth gained from a preceding demontration.

A Lemma is the demontration of some premie, whereby the proof of the thing in hand becomes the horter.

Rom any point to any point to draw a right line.

2. To produce a right line finite, trait forth continually.

3. Upon any center, and at any ditance, to decribe a circle.

Hings equal to the ame third, are alo equal one to the other.

As A=B=C. Therefore A=C. Or therefore all, A, B, C, are equal the one to the other.

Note, When everal quantities are joined the one to the other continually with this mark =, the firt quantity is by virtue of this axiome equal to the lat, and every one to every one: In which cae we often