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" When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands. "
Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books - Side 18
av Euclid - 1765 - 464 sider
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Classics in the History of Greek Mathematics

Jean Christianidis - 2004 - 474 sider
...perpendicular to AT and Definition I.10, which states that “When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the right angles is right, and the straight line standing on the other is called a perpendicular to that...
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Euclid's Elements in Greek: Vol. I:

Richard Fitzpatrick - 2005 - 296 sider
...EC F [Prop. 1.8], and they are adjacent. But when a straight-line stood on a(nother) straight-line makes the adjacent angles equal to one another, each of the equal angles is a right-angle [Def. 1.10]. Thus, each of the (angles) DGF and FCE is a right-angle. Thus, the straight-line...
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Visualization, Explanation and Reasoning Styles in Mathematics

Paolo Mancosu, Klaus Frovin Jørgensen, S.A. Pedersen, Stig Andur Pedersen - 2005 - 300 sider
...of (rectilinear) angles (trans. Heath 1926, I, 181): 1 0. When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right [...]. 1 1 . An obtuse angle is an angle greater than a right angle. 12. An acute angle is an...
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The Thirteen Books of Euclib's Elements.

Euclid
...ptifav opOrji. 12. "O£«ia Si 17 l\ti<T(Tu>v 6p6rj<;. v- 10. fffo/ia straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, anil the straight line standing on the other is called a perpendicular to that on which it stands....
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - 1998 - 488 sider
...is not necessary to define a rectilineal angle). 10. SJt When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands....
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The Thirteen Books of Euclid's Elements

Euclid
...therefore the angle AFE is equal to the angle BFE. [i. 8] But, when a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right ; [i. Def. 10] 20 therefore each of the angles AFE, BFE is right. Therefore CD, which is through...
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Euclid in Greek, Volum 1

Euclid - 1920 - 239 sider
...line on which it stands.' The full translation then is: 'When a straight line set up on a straight line makes the adjacent angles equal to one another, each of the equal angles is right, and the straight line standing on the other is called a perpendicular to that on which it stands.'...
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