Definitions
A breadthless length
What is a line?
That all right angles are equal to one another
What is Postulate 4?
To place at a given point as an extremity a straight line equal to a given straight line.
What is Prop 2?
Prop 1 given
What is a finite straight line?
It is fitting that when Mr. Hansen talks about this, it feels like he's going on for forever.
What is the infinite?
Then the angle is called rectilineal
What is when the lines containing the angle are straight?
Postulate 1
What is to draw a straight line from any point to any point?
Prop 10 lets us do this
What is bisect a given finite straight line?
Prop 9 to prove
What is to bisect a given rectilineal angle
This branch of mathematics was discovered by Leibniz and Newton. You will study it during your time at Great Hearts
What is Calculus?
That which is an extremity of anything
What is a boundary?
Common Notion 3
What is If equals be subtracted from equals then the remainders are equal?
These propositions show Side Angle Side Theorem and Side Side Side Theorem.
What are props 4 and 8?
You're given a triangle with two equal angles in this prop
What is prop 6?
Any 4 of the Liberal Arts
What are Geometry, Astronomy, Music, Arithmetic, Logic, Grammar, and Rhetoric?
That which has its three sides unequal
What is a scalene triangle?
This happens when a straight line is set up on two straight lines and the interior angles don't add up to two rights
What is meet on that side?
These two propositions are converses of one another
What are props 5 and 6?
We prove this in prop 16
Plato's most famous allegory in the Republic
What is the cave?
That which has its opposite sides and angles equal to one another but is neither equilateral nor right-angled
What is a rhomboid?
Common Notion 4
What is things which coincide with one another are equal to one another
Prop 12 is the first time we formally encounter this in a proof.
What is the infinite?
When proving this prop, you also prove a porism. Double the points if you can state the porism.
What is prop 15? Porism: If two straight lines cut one another they will make the angles at the point of section equal to four right angles
The inscription outside of Plato's Academy said this
What is Let no one ignorant of geometry enter.