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" The straight line drawn at right angles to the diameter of a circle, from the extremity of it, falls without the circle... "
The Cambridge Examiner - Page 257
1881
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...angle less than any rectilineal angle.' Cor. From this it is manifest, that the straight line which is drawn at right angles to the diameter of a circle from the extremity of it, touches the circle ; and (hat it touches it only in one point, because, if it did meet the circle in...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 234 pages
...and the remaining angle less than any rectilineal angle. QED Deductions. 1. The right line which is drawn at right angles to the diameter of a circle from the extremity of it touches the circle, and that it touches only in one point. 2. To describe a circle, which shall touch...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...and the remaining angle less than any .rectilineal angle. QED Deductions. 1. The right line which is drawn at right angles to the diameter of a circle from the extremity of it touches the circle, and that it touches only in one point. 2. To describe a circle, which shall touch...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...of EK, and the straight lineliHless than EK. Whereforq, the diameter, &$, QE J). PROP. XVI. THEOR. The straight line drawn at right angles to the diameter of a eirele, from the extremity of it, falls without the circle ; and no straight line ean be drawn between...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...D. PROP. XVI. THEOR. The straight line drawn at right angles to the diameter of See N. a circle,from the extremity of it, falls without the circle ; and...and the circumference, so as not to cut the circle -, or, which is the same thing, no straight line can make so great an acute angle with the diameter...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 pages
...nearer t to the centre than FG. Wherefore, the diameter, &c. y. ED PROPOSITION XVI. See N. THEOR. — The straight line drawn at right angles to the diameter of a circle, from the extremity of it, Jails without the circle ; and no straight line can be drawn from the extremity, between that straight...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...less than " any rectilineal angle." COR. From this it is manifest, that the straight line whick is drawn at right angles to the diameter of a circle from the extremity of it, touches the circle ; and that it touches it only in one point, because, if it did meet the circle in...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...is always greater than the more remote; and the greater is nearer to the centre than the less. XVI. The straight line drawn at right angles to the diameter of a circle, from the extremity of it, fulls without the circle ; and no straight line can be drawn between that straight line and the circumference,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 488 pages
...of EK, and the straight line EH less than EK. Wherefore the diameter, &c. QED PROP. XVI. THEOR. iTke straight line drawn at right angles to the diameter of a circle, from the extremity of zY, falls without the circle ; and no straight line can be drawn between that straight line and the...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 112 pages
...that BH > FK, 2. that EH" < EK" and .'. EH < EK. PROPOSITION XVI. (Argument ad absurdum). Theorem. The straight line drawn at right angles to the diameter...without the circle; and no straight line can be drawn between that straight line and the circumference from the extremity, so as not to cut the circle. Steps...
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