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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... "
Elements of Geometry: Containing the First Six Books of Euclid: With a ... - Side 77
av John Playfair - 1819 - 317 sider
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...diameter AC, is a tangent to the circle ; and no straight line can be drawn between the tangent and circumference, from the extremity of the diameter, so as not to cut the circle. Let B be any point in the straight line AB, join this point and the centre D. Then, because DAB is a right...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...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 no straight line can be drawn from the extremity, between that straight line and the circumference, so as not to cut the circle -,...
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The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - 1829 - 516 sider
...square of EK, and the straight line EH less than EK. .Wherefore the diameter, &c. QED PROP. XVI. THEOR. THE straight line drawn at right angles to the diameter...between that straight line and the circumference from ther extremity, so as not to cut the circle ; or which is the same thing, no straight line can make...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...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 ...

Robert Simson - 1835 - 513 sider
...diameter," &c. QED PROP. XVI. THEOR. The straight line drawn at right angles to the dia- See N. meter of a circle, from the extremity of it, falls without...extremity of the diameter, 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 at...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...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 ...

1836 - 472 sider
...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 - 1837 - 318 sider
...centre ; and, conversely, the farther the chord is from the centre, the shorter it is. PROP. XVI. THEOR. The straight line drawn at right angles to the diameter...extremity of the diameter, so as not to cut the circle. In AE take any point F, join DF and let DF meet the circle in C. Because DAF is a right angle, it is...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...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...straight line and the circumference from the extremity, so as not to cut the circle. Steps of the Demonstration. Part 1st. That the right line from the extremity...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...of EK, and the straight line EH less than EK. Wherefore the diameter, &c. Q,. ED , PROP. XVI. THEOR. THE straight line drawn at right angles to the diameter of a circle, from the extremity of if, falls without the circle ; and no straight line can be drawn between that straight line and the...
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