— GEOMETOR • elements

G.247 unit

An:term:**unit** <unit> is that by virtue of which each of the things that exist is called one.

G.248 number

A:term:**number** <number> is a multitude composed of:term:units <G.247>.

G.249 numbers prime to one another

Numbers prime to one another are those which are:term:measured <G.253> by an:term:unit <G.247> alone as a common measure.

Two unequal numbers being set out, and the less being continually subtracted in turn from the greater, if the number which is left never measures the one before it until an unit is left, the original numbers is prime to one another.

G.251 numbers prime find

Given two numbers not prime to one another, to find their greatest common measure.

G.255 number part parts

Any number is either a part or parts of any number, the less of the greater.

G.268 unit measure number

If an unit measure any number, and another number measure any other number the same number of times, alternately also, the unit will measure the third number the same number of times that the second measures the fourth.

G.269 multiplication of numbers

A:term:number <G.248> is said to:term:**multiply** <multiply> a number when that which is multiplied is added to itself as many times as there are:term:units <G.247> in the other, and thus some number is produced.

G.270 numbers multiplying make

If two numbers by multiplying one another make certain numbers, the numbers so produced are equal.

G.271 number multiplying numbers

If a number by multiplying two numbers make certain numbers, the numbers so produced will have the same ratio as the numbers multiplied.

G.275 numbers prime least

Numbers prime to one another are the least of those which have the same ratio with them.

G.276 least numbers ratio

The least numbers of those which have the same ratio with them are prime to one another.

G.278 numbers prime number

If two numbers be prime to any number, their product also is prime to the same.

G.283 prime number

A:term:**prime number** <prime-number> is that which is:term:measured <G.253> by an:term:unit <G.247> alone.

G.285 numbers multiplying make

If two numbers by multiplying one another make some number, and any prime number measure the product, it will also measure one of the original numbers.

G.289 many numbers please

Given as many numbers as we please, to find the least of those which have the same ratio with them.

G.290 numbers find least

Given two numbers, to find the least number which they measure.

G.293 number measured number

If a number be measured by any number, the number which is measured will have a part called by the same name as the measuring number.

G.294 number part whatever

If a number have any part whatever, it is measured by a number called by the same name as the part.

G.303 there many numbers

If there be as many numbers as we please in continued proportion, and the first do not measure the second, neither will any other measure any other.

G.306 numbers prime numbers

If two numbers be prime to one another, and numbers fall between them in continued proportion, then, however many numbers fall between them in continued proportion, so many will also fall between each of them and an unit in continued proportion.

G.307 numbers fall numbers

If numbers fall between each of two numbers and an unit in continued proportion, however many numbers fall between each of them and an unit in continued proportion, so many also will fall between the numbers themselves in continued proportion.

G.322 mean proportional number

If one mean proportional number fall between two numbers, the numbers is similar plane numbers.

G.323 mean proportional numbers

If two mean proportional numbers fall between two numbers, the numbers are similar solid numbers.

G.332 cube number multiplying

If a cube number by multiplying itself make some number, the product is cube.

G.335 number multiplying itself

If a number by multiplying itself make a cube number, it will itself also be cube.

G.336 composite number multiplying

If a composite number by multiplying any number make some number, the product is solid.

G.337 many numbers please

If as many numbers as we please beginning from an unit be in continued proportion, the third from the unit is square, as will also those which successively leave out one; the fourth is cube, as will also all those which leave out two; and the seventh is at once cube and square, as will also those which leave out five.

G.338 many numbers please

If as many numbers as we please beginning from an unit be in continued proportion, and the number after the unit be square, all the rest is square. And, if the number after the unit be cube, all the rest is cube.

G.339 many numbers please

If as many numbers as we please beginning from an unit be in continued proportion, and the number after the unit be not square, neither will any other be square except the third from the unit and all those which leave out one. And, if the number after the unit be not cube, neither will any other be cube except the fourth from the unit and all those which leave out two.

Posts tagged 'unit'