Euclid's Elements: Proposition 7

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In summary, the conversation is about a person who is reading Euclid's Elements and is stuck on proposition 7. They are having trouble understanding the reasoning behind the statement that "the angle ADC is greater than the angle DCB; therefore the angle CDB is much greater than the angle DCB." They mention being able to understand the basic concept of the proposition but struggle with the assumption that angle CDB must be greater than DCB. The link to the proposition is also provided.
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AntiMe
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Alright so, I decided to read some Euclid's Elements for my own personal gain (became interested while reading Stewart's Precal, and I think it might help with Calculus) and I'm stuck on proposition 7, mainly because I really want to understand the reasoning behind it and I just can't seem to make a connection.I pretty much understand the basis of what proposition 7 is trying to prove or demonstrate, but I just can't get around the fact that in the statement that "the angle ADC is greater than the angle DCB; therefore the angle CDB is much greater than the angle DCB" doesn't make sense to me. ADC is not equal to CDB.

Maybe I'm just too stupid to understand, but where is the assumption that angle CDB must be greater than DCB made plausible?

Here is the link to the proposition
 
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  • #2
CDB is greater than CDA, which equals DCA, which is greater than DCB. Thus CDB is "much" greater than DCB.
 

Related to Euclid's Elements: Proposition 7

What is Euclid's Elements: Proposition 7?

Euclid's Elements is a mathematical treatise written by the ancient Greek mathematician Euclid, which is considered to be one of the most influential works in the history of mathematics. Proposition 7, also known as the Pythagorean Theorem, is one of the most well-known and important propositions in the book.

What does Proposition 7 state?

Proposition 7 states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

How is Proposition 7 proven?

Proposition 7 is proven using a series of geometric constructions and logical deductions. Euclid's method of proof is known as deductive reasoning, where the truth of the conclusion is guaranteed by the truth of the statements that came before it.

Why is Proposition 7 important?

Proposition 7, or the Pythagorean Theorem, is important because it has numerous applications in geometry, trigonometry, and other branches of mathematics. It is also used in many real-world problems, such as calculating distances and areas.

Are there any other versions of Proposition 7?

Yes, there are multiple versions of Proposition 7 that have been discovered by mathematicians throughout history. These include algebraic, geometric, and trigonometric proofs, as well as generalizations of the theorem to higher dimensions.

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