Depending on whether it is a problem or a theorem, a proposition has up to 6 parts.

**Proposition**: General enunciation of the problem to be done or theorem to be demonstrated.**Exposition**: Particular enunciation of what is given.**Determination**: Particular enunciation of what is sought.**Construction**: Diagram of the proposition.**Demonstration**: Syllogisms by which the proposition is proven.**Conclusion**: Recapitulation of the Proposition.

The six parts of a proposition are labeled in the proposition below:

**The Syllogisms of the Demonstration**

The Demonstration is composed of syllogisms based on the definitions and axioms given at the beginning of the book, or on previously demonstrated propositions.

- Syllogism 1
- Definition of a Circle
- Point A is center of Circle BCD
- AC must be equal to AB

- Syllogism 2
- Definition of a Circle
- Point B is center of Circle ACE
- BC must be equal to AB

- Syllogism 3
- Axiom 1
- AC and BC are equal to AB
- AC must be equal to BC

- Syllogism 4
- Definition of Equil. Triangle
- AB, AC, BC are equal
- ABC must be an Equilateral Triangle (QEF)

God bless,

William Michael, Headmaster

Classical Liberal Arts Academy

## Comments

0 comments

Please sign in to leave a comment.