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revert several edits. this sixth common notion doesn't match the most common editions and I'm not sure where it comes from, maybe take it to the talk page. Other minor changes seem like disimprovements, but I left "in" -> "for" (though "in" was also fine; it is common to use an author's name to stand for the work), and changed an "e.g." to "for instance" |
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In modern terminology, angles would normally be measured in [[degree (angle)|degree]]s or [[radian]]s.
Modern school textbooks often define separate figures called [[line (geometry)|line]]s (infinite), [[Line (mathematics)#Ray|rays]] (semi-infinite), and [[line segment]]s (of finite length). Euclid, rather than discussing a ray as an object that extends to infinity in one direction, would normally use locutions such as "if the line is extended to a sufficient length", although he occasionally referred to "infinite lines". A "line"
== Some important or well known results ==
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===Scaling of area and volume===
In modern terminology, the area of a plane figure is proportional to the square of any of its linear dimensions, <math>A \propto L^2</math>, and the volume of a solid to the cube, <math>V \propto L^3</math>. Euclid proved these results in various special cases such as the area of a circle<ref>Euclid, book XII, proposition 2.</ref> and the volume of a parallelepipedal solid.<ref>Euclid, book XI, proposition 33.</ref> Euclid determined some, but not all, of the relevant constants of proportionality.
==System of measurement and arithmetic==
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