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24 Cards in this Set
- Front
- Back
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Postulate 1
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It is possible to draw a straight line between and two given points.
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Postulate 2
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It is possible to produce a finite straight line indefinitely.
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Postulate 3
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It is possible to draw a circle given any point and radius.
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Postulate 4
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All right angles are equal to each other.
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Postulate 5
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If a straight line is drawn to intersect two given straight lines such that on one side (side A) of the straight line, the sum of the interior angles are less than two right angles, then the two given straight lines when produced indefinitely meet on side A.
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How many postulates are there
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5
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How many books are there?
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13
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What is in book 1?
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23 definitions
5 postulates 5 more axioms |
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What did Euclid call axioms?
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Common Notions
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What is in book 2?
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parallelograms, triangles, rectangles and squares
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What is in book 3?
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Circles
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What is in book 4?
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Inscription and circumscription of triangles and regular polygons
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What is in books 5-6?
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Eudoxus' Theory of Proportions
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What is in books 7-9?
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Number Theory
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What is in book 10?
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Rational and Irrational Numbers - root 2
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What is in books 11-13?
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The 5 Platonic Solids
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Proposition 31 (book 1)
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Given a straight line and a point off of that line, we can construct a straight line that is parallel to the given line and goes through the point.
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Playfair's Axiom
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Only one line (through a point off the given line) can be drawn parallel to the given line.
(A corollary to proposition 31) |
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Proposition 29 (Book 1)
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A straight line falling on parallel straight lines makes the alternate angles equal to one another, the exterior angle equal to the interior and opposite angle, and the sum of the interior angles on the same side equal to two right angles.
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Axiom/common notion 1
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Things which are equal to the same thing are also equal to one another.
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Axiom/common notion 2
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If equals be added to equals, the wholes are equal.
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Axiom/common notion 3
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If equals be subtracted from equals, the remainders are equal.
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Axiom/common notion 4
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Things which coincide with one another are equal to one another.
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Axiom/common notion 5
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The whole is greater than the part.
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