THE straight line drawn at right angles to the diameter of a circle, from the extremity of... Books 3-9 - Page 37by Euclid, Sir Thomas Little Heath, Johan Ludvig Heiberg - 1908Full view - About this book
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| Euclides - 2005
...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... | |
| 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... | |
| Euclid
...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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