Category:Definitions/Apotome
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This category contains definitions related to Apotome.
Related results can be found in Category:Apotome.
Let $a, b \in \set {x \in \R_{>0} : x^2 \in \Q}$ be two rationally expressible numbers such that $a > b$.
Then $a - b$ is an apotome if and only if:
- $(1): \quad \dfrac a b \notin \Q$
- $(2): \quad \paren {\dfrac a b}^2 \in \Q$
where $\Q$ denotes the set of rational numbers.
In the words of Euclid:
- If from a rational straight line there be subtracted a rational straight line commensurable with the whole in square only, the remainder is irrational; and let it be called an apotome.
Pages in category "Definitions/Apotome"
The following 34 pages are in this category, out of 34 total.
A
- Definition:Annex of Apotome
- Definition:Annex of Apotome of Medial
- Definition:Apotome
- Definition:Apotome of Medial
- Definition:Apotome of Medial/Annex
- Definition:Apotome of Medial/First Apotome
- Definition:Apotome of Medial/Order
- Definition:Apotome of Medial/Second Apotome
- Definition:Apotome of Medial/Terms
- Definition:Apotome of Medial/Whole
- Definition:Apotome/Annex
- Definition:Apotome/Fifth Apotome
- Definition:Apotome/First Apotome
- Definition:Apotome/Fourth Apotome
- Definition:Apotome/Order
- Definition:Apotome/Second Apotome
- Definition:Apotome/Sixth Apotome
- Definition:Apotome/Terms
- Definition:Apotome/Third Apotome
- Definition:Apotome/Warning
- Definition:Apotome/Whole