XXXVI. In a Parallelogram ABCD, when a diameter AC, and two lines EF, HI parallel to the ſides, cutting the diameter in one and the ſame point G, are drawn, ſo that the Parallelogram be divided by them into four parallelograms; thoſe two DG, GB, through which the diameter paſſeth not, are called Complements; and the other two HE, FI, through which the diameter paſſeth, the Parallelograms ſtanding about the diameter.
A Problem is, when ſomething is propoſed to be done or effected.
A Theoreme is, when ſomething is propoſed to be demonſtrated.
A Corollary is a conſectary, or ſome conſequent truth gained from a preceding demonſtration.
A Lemma is the demonſtration of some premiſe, whereby the proof of the thing in hand becomes the ſhorter.
Poſtulates or Petitions.
1. FRom any point to any point to draw a right line.
2. To produce a right line finite, ſtrait forth continually.
3. Upon any center, and at any diſtance, to deſcribe a circle.
Axioms.
1. THings equal to the ſame third, are alſo 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 ſeveral quantities are joined the one to the other continually with this mark =, the firſt quantity is by virtue of this axiome equal to the laſt, and every one to every one: In which caſe we often ab-
