Things to Know:
Jacob's definition of a postulate:
A postulate is a statement that is assumed to be true without proof (page 40).Jacob calls some terms "undefined" meaning that if you attempt to define them you will go in circles. Euclid tries to start with as little as possible and build from there, which is the classical way of doing things .... look at his definitions
Look at these first postulates of Euclid's -- many of them are constructions, which means that Euclid asks that we draw them or at least agree that they can be drawn. Postulates are also called axioms.... see here. Wikipedia says:
In traditional logic, an axiom or postulate is a proposition that is not proved or demonstrated but considered to be either self-evident, or subject to necessary decision. Therefore, its truth is taken for granted, and serves as a starting point for deducing and inferring other (theory dependent) truths.
In this course we are going to start at the end of each chapter, since Jacob sums up what he has covered and this can be useful.
Turn to page 79
There is a list of postulates. Take a pencil and try to draw the postulates. This will probably help you understand them better since they won't be just abstract sentences. If you need help, ask.
Jacobs defines a theorem this way:
A theorem is a statement that is proved by reasoning deductively from already accepted statements.
Look at the theorems on page 79 and see if they seem to make sense given the postulates.
To DO:
Try this quiz. Hint: the proportions should match.
KTR
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