Theory of Proportions - what is it?

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In summary, the conversation is about the concept of theory of proportions in mathematics and how it relates to setting ratios equal to each other. The person is struggling to understand this concept and has tried searching online for more information.
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genericusrnme
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I've recently got back into studying maths in my own time and I've come across this (see attached image)
The middle line.. I put some numbers in there and those equalities do not hold..
I don't see why we can set everything there equal..
Could someone explain this to me or at least point me in the right direction?
I've tried googling theory of proportions but all I've managed to get was chemistry related stuff

I was having a good night of study until that came up as well :(

Thanks in advance
 

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Related to Theory of Proportions - what is it?

1. What is the Theory of Proportions?

The Theory of Proportions is a mathematical concept that deals with the relationship between different quantities or magnitudes. It states that the ratio between two quantities remains constant even when their values change. It is based on the idea of proportionality, where one quantity is directly or inversely related to another.

2. Who developed the Theory of Proportions?

The Theory of Proportions was first developed by the ancient Greek mathematician, Euclid. He included it in his famous work, "Elements", which laid the foundation for modern geometry. Later on, other mathematicians such as Archimedes and Leonardo da Vinci also contributed to the development of this theory.

3. What are the applications of the Theory of Proportions?

The Theory of Proportions has various applications in different fields such as mathematics, science, engineering, and economics. It is used to solve problems related to ratios, scaling, and similarity. It is also used to design and construct structures, analyze data, and make predictions.

4. How is the Theory of Proportions different from the Theory of Ratios?

The Theory of Proportions and the Theory of Ratios are often used interchangeably, but there is a slight difference between them. The Theory of Proportions deals with the relationship between two quantities that are of the same kind, while the Theory of Ratios deals with the relationship between two quantities that are of different kinds. In simple terms, proportion compares two values of the same unit, while ratio compares two values of different units.

5. Can the Theory of Proportions be applied to real-life situations?

Yes, the Theory of Proportions can be applied to various real-life situations. For example, it is used in cooking to measure ingredients, in photography to adjust the size of images, and in finance to calculate interest rates. It is also used in everyday tasks such as mixing drinks, resizing images, and converting currency.

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