Posts tagged 'prime'
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.
G.250 unequal numbers set
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.252 numbers prime find
Given three numbers not prime to one another, to find their greatest common measure.
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.277 numbers prime number
If two numbers be prime to one another, the number which measures the one of them is prime to the remaining number.
G.278 numbers prime number
If two numbers be prime to any number, their product also is prime to the same.
G.279 numbers prime product
If two numbers be prime to one another, the product of one of them into itself is prime to the remaining one.
G.280 numbers prime numbers
If two numbers be prime to two numbers, both to each, their products also is prime to one another.
G.281 numbers prime multiplying
If two numbers be prime to one another, and each by multiplying itself make a certain number, the products is prime to one another; and, if the original numbers by multiplying the products make certain numbers, the latter is prime to one another [and this is always the case with the extremes].
G.282 numbers prime sum
If two numbers be prime to one another, the sum is prime to each of them; and, if the sum of two numbers be prime to any one of them, the original numbers is prime to one another.
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.284 prime number prime
Any prime number is prime to any number which it does not measure.
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.287 composite number measured
Any composite number is measured by some prime number.
G.288 number prime measured
Any number either is prime or is measured by some prime number.
G.296 there many numbers
If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the numbers are the least of those which have the same ratio with them.
G.298 many numbers please
If as many numbers as we please in continued proportion be the least of those which have the same ratio with them, the extremes of them are prime to one another.
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.342 many numbers please
If as many numbers as we please beginning from an unit be in continued proportion, by however many prime numbers the last is measured, the next to the unit is measured by the same.
G.343 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 prime, the greatest will not be measured by any except those which have a place among the proportional numbers.
G.344 number least measured
If a number be the least that is measured by prime numbers, it will not be measured by any other prime number except those originally measuring it.
G.345 numbers continued proportion
If three numbers in continued proportion be the least of those which have the same ratio with them, any two whatever added together is prime to the remaining number.
G.346 numbers prime number
If two numbers be prime to one another, the second will not be to any other number as the first is to the second.
G.347 there many numbers
If there be as many numbers as we please in continued proportion, and the extremes of them be prime to one another, the last will not be to any other number as the first to the second.
G.350 prime numbers more
Prime numbers are more than any assigned multitude of prime numbers.
G.362 odd number prime
If an odd number be prime to any number, it is prime to the double of it.
G.370 many numbers please
If as many numbers as we please beginning from an unit be set out continuously in double proportion, until the sum of all becomes prime, and if the sum multiplied into the last make some number, the product is perfect.