G.288 number prime measured — Heath

VII.32

Any number either is prime or is measured by some prime number.

Let A be a number;

I say that A either is prime or is measured by some prime number.

If now A is prime, that which was enjoined will have been done.
A
[G.287]But if it is composite, some prime number will measure it.
Therefore any number either is prime or is measured by some prime number.
Q. E. D.

Dependency Graph

digraph { bgcolor="transparent"; node [shape=box, style="rounded,filled", fontname="Helvetica", fontsize=11, color="#d6d3cd", fontcolor="#ffffff"]; edge [color="#8c857b", fontcolor="#8c857b", arrowsize=0.75]; rankdir="TB"; "G.169" [label="G.169", tooltip="G.169 (V.def.1): A magnitude is apart of a magnitude, the less of the greater, when it measures the greater.", fillcolor="#224422", URL="../G.169/index.html", target="_top"]; "G.247" [label="G.247", tooltip="G.247 (VII.def.1): Anunit is that by virtue of which each of the things that exist is called one.", fillcolor="#224422", URL="../G.247/index.html", target="_top"]; "G.248" [label="G.248", tooltip="G.248 (VII.def.2): Anumber is a multitude composed ofunits.", fillcolor="#224422", URL="../G.248/index.html", target="_top"]; "G.253" [label="G.253", tooltip="G.253 (VII.def.3): Anumber is apart of a number, the less of the greater, when itmeasures the greater;", fillcolor="#224422", URL="../G.253/index.html", target="_top"]; "G.283" [label="G.283", tooltip="G.283 (VII.def.11): Aprime number is that which ismeasured by anunit alone.", fillcolor="#224422", URL="../G.283/index.html", target="_top"]; "G.286" [label="G.286", tooltip="G.286 (VII.def.13): Acomposite number is that which ismeasured by somenumber.", fillcolor="#224422", URL="../G.286/index.html", target="_top"]; "G.287" [label="G.287", tooltip="G.287 (VII.31): Any composite number is measured by some prime number.", fillcolor="#222244", URL="../G.287/index.html", target="_top"]; "G.288" [label="G.288", tooltip="G.288 (VII.32): Any number either is prime or is measured by some prime number.", penwidth=2.5, color="#e8b85a", fillcolor="#4a453b", URL="index.html", target="_top"]; "G.253" -> "G.169"; "G.283" -> "G.169"; "G.286" -> "G.169"; "G.287" -> "G.169"; "G.288" -> "G.169"; "G.248" -> "G.247"; "G.283" -> "G.247"; "G.253" -> "G.248"; "G.286" -> "G.248"; "G.287" -> "G.248"; "G.288" -> "G.248"; "G.283" -> "G.253"; "G.286" -> "G.253"; "G.287" -> "G.283"; "G.288" -> "G.283"; "G.287" -> "G.286"; "G.288" -> "G.286"; "G.288" -> "G.287"; }