Extemporaneous musings, occasionally poetic, about life in its richly varied dimensions, especially as relates to history, theology, law, literature, science, by one who is an attorney, ordained minister, historian, writer, and African American.
Saturday, December 8, 2018
LIFE IS A PRIME NUMBER
Every male and female is a prime number relatively speaking. This proposition is proven in Euclid's geometry, book 7, proposition 1, to wit:
Proposition 1
When two unequal numbers are set out, and the less is continually subtracted in turn from the greater, if the number which is left never measures the one before it until a unit is left, then the original numbers are relatively prime.
The less of two unequal numbers AB and CD being continually subtracted from the greater, let the number which is left never measure the one before it until a unit is left.
java applet or image VII.Def.12
I say that AB and CD are relatively prime, that is, that a unit alone measures AB and CD.
If AB and CD are not relatively prime, then some number E measures them. Let CD, measuring BF, leave FA less than itself, let AF, measuring DG, leave GC less than itself, and let GC, measuring FH, leave a unit HA.
Since, then, E measures CD, and CD measures BF, therefore E also measures BF.
But it also measures the whole BA, therefore it measures the remainder AF. But AF measures DG, therefore E also measures DG. But it also measures the whole DC, therefore it also measures the remainder CG.
But CG measures FH, therefore E also measures FH. But it also measures the whole FA, therefore it measures the remainder, the unit AH, though it is a number, which is impossible.
VII.Def.12
Therefore no number measures the numbers AB and CD. Therefore AB and CD are relatively prime.
Therefore, when two unequal numbers are set out, and the less is continually subtracted in turn from the greater, if the number which is left never measures the one before it until a unit is left, then the original numbers are relatively prime.
Q.E.D.
https://mathcs.clarku.edu/~djoyce/elements/bookVII/propVII1.html?fbclid=IwAR2z3GjwXw4KPAAS5NM0untt51Kr9lXk5kMwCyrqzegcgUdEBHR-JFhVQzs