# Euclid

## Euclid's Theorem

All of Euclid’s ratios are pure ratios of two magnitudes of the same kind, in other words, there are no mixed ratios in the Elements. A familiar example of a mixed ratio is velocity, the ratio of a distance to a time, measured in units such as kilometers/hour. That isn’t to say that ratios of different kinds of magnitudes aren’t equated. In fact, that’s one of the more important aspects of ratios. For example, the fundamental proposition of Book VI, proposition VI.1, says that given two triangles of the same height, the ratio of the triangles A : B is the same as the ratio of their heights Ah:Bh. That says that the ratio of two plane figures equals the ratio of two lines.

## Easier To Understand Euclid's Theorem

A ratio is how we can compare two things using numbers. When we compare, we are able to show the proportion of food, people, size, or numbers. If a class has a teacher with 23 students, the ratio is 1:23. (1 teacher to 23 students).

## Real World Use

We use ratios in businesses when they compare numbers in stats. They use it to collect and analyze data that has really big numbers. Construction workers, builders and architects use this to make plans for building a new structure. Anyone in food preparation uses ratios to prepare different foods. All grocery shoppers uses ratios as they compare different brands of the same foods. They will look at how many ounces of cereal may be in the two boxes. This helps them compare prices, so they can buy the box of cereal for the better deal. Also, classroom teachers use ratios, so the number of students is known to the teachers available at different times of the school day.