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Books Books 71 - 80 of 81 on THE straight line drawn at right angles to the diameter of a circle, from the extremity....
" THE straight line drawn at right angles to the diameter of a circle, from the extremity of... "
Books 3-9 - Page 37
by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908
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A Source Book in Medieval Science, Volume 1

Edward Grant - History - 1974 - 864 pages
...composed of indivisibles. 1 1. That is III. 16 of the Greek Euclid, the relevant portion of which reads: "The straight line drawn at right angles to the diameter...circle from its extremity will fall outside the circle. ..." 12. Which reads: "If a straight line set up on a straight line make angles, it will make either...
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Henry More. The Immortality of the Soul: Edited with an Introduction and Notes

A. Jacob - History - 1987 - 468 pages
...of Imagination: 'See Antidote, Book I, Ch 4, sect 2' [M]. 25/42 Euclide:Elements,Bk.lll, Prop. 16: 'The straight line drawn at right angles to the diameter...remaining angle less, than any acute rectilineal angle.' The perplexity of this proposition is attested by the long controversy related to it from antiquity...
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Mathematical Thought from Ancient to Modern Times:

Morris Kline - Mathematics - 1990 - 390 pages
...to us from high school geometry. The following theorems are worthy of special note. Proposition 1 6. The straight line drawn at right angles to the diameter...greater, and the remaining angle less, than any acute rectilinear angle. The novelty in the theorem is that Euclid considers the space (Fig. 4,12) between...
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The Scientific Letters and Papers of James Clerk Maxwell: 1846-1862

James Clerk Maxwell - Electromagnetic theory - 1990 - 748 pages
...powers of the foci. See Figs. [3,24, 3,25]. (16) Book III, Prop. XVI of Euclid's Elements: (Theorem) 'The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle; and no straight line can be drawn between that straight...
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Vita Mathematica: Historical Research and Integration with Teaching

Ronald Calinger - Mathematics - 1996 - 359 pages
...advantage of avoiding any reference to the infinite. In Elements III, 16, for example, Euclid proves that "the straight line drawn at right angles to the diameter...a circle from its extremity will fall outside the circle."23 To do this, he supposes that the straight line AE falls inside the circle, like AC. This...
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The Cambridge Companion to Galileo

Peter Machamer - Philosophy - 1998 - 462 pages
...Archive for the History of Exact Sciences, 1990,41/1:115-37. 93 Heath, Euclid's Elements, III, 16: "The straight line drawn at right angles to the diameter...greater, and the remaining angle less than any acute rectilinear angle." X, 1: "Two unequal magnitudes set out, if from the greater there be substracted...
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Conflicts Between Generalization, Rigor, and Intuition: Number Concepts ...

Gert Schubring - Mathematics - 2005 - 678 pages
...in Book III, 16. This proposition has subsequently provoked an extensive debate, however. It says: The straight line drawn at right angles to the diameter...greater, and the remaining angle less, than any acute rectilinear angle (Heath, vol. II, 37). Proclus, in his commentary on Euclid, rejected this assumed...
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Campanus of Novara and Euclid's Elements, Volumes 1-2

Euclides, Johannes Campanus - Mathematics - 2005 - 768 pages
...remaining angle less, than any acute rectilineal angle", and to the porism "From this it is manifest that the straight line drawn at right angles to the diameter of a circle from its extremity touches the circle", the author of the Savile text only remarks: Reliqua autem diligentie lectoris...
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Euclid in China: The Genesis of the First Chinese Translation of Euclid's ...

Peter M. Engelfriet - Mathematics - 1998 - 488 pages
...of Euclid.7 Theorem 16 of Book III says the following: ft (P. 693) ! ft ft W Ji ft 'h T- & a Heath The straight line drawn at right angles to the diameter...greater, and the remaining angle less, than any acute rectlineal angle. (The "straight-angle-line" at the end of the diameter of the circle is entirely outside...
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The Thirteen Books of Euclid's Elements, Volume 2, Books 3-9

Euclides - 1956
...angle EBA. But the angle EDF is right ; therefore the angle EBA is also right. Now EB is a radius ; and the straight line drawn at right angles to the diameter of a circle, from its extremity, touches the circle ; [m. 16, For.] therefore AB touches the circle BCD. Therefore from the given point...
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