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" If a straight line drawn through the centre of a circle bisect a straight line in it which does not pass through the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it. "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Page 11
by Euclides - 1861
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1806 - 311 pages
...within the circle. Wherefore, if any two points, &c. QED a 1.3. b5. c 16. 1. A 19. 1. PROP. III. THEOR. IF a straight line drawn through the centre of a circle bisect a straight line in the circle, which does not pass through the centre, it will cut that line at right angles ; and if...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Euclid's Elements - 1806 - 518 pages
...B ^""~- *^x" C b 3. ; right angle: again, because the straight line FE bisects the straight line BD which does not pass through the centre, it shall cut it at rightb angles : wherefore FEB is a right angle : and FEA was shown to be a right angle ; therefore...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...them shall fall within the circle. Prop. III. Theor. If a straight Hue drawn through the еешге of a circle bisect a straight line in it which does...the centre, it shall cut it at right angles; and, if it cuts it alright angles, it shall bisect it. Prop. IV. Theor. If in a circle two straight lines...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Euclid's Elements - 1816 - 528 pages
...of the circle, and join EF; and because FE, a straight line through the centre, bisects another AC which does not pass through the centre, it shall cut it at right b angles ; where- * 3. 3. fore FEA is a right angle : Again, because the straight line FE bisects the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...therefore AB is within the circle. Wherefore, if any two points, &,c. Q,. ED PROP. III. THEOR. ^fa straight line drawn through the centre of a circle bisect a straight line in the circle, which does not pass through the centre, it wilt cut that line at right angles ; and if...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...B, therefore AB is within the circle. Wherefore, if any two points, &c. Q, ED PROP. III. THEOR, //' a straight line drawn through the centre of a circle bisect a straight lineinlhe circle, which does not pass through the centre, it will cut that line at right angles ; and...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 516 pages
...circumference; it falls therefore within it. Wherefore, if any two points, &c. QED . III. THEOR. IP a straight line drawn through the centre of a circle...the centre, it shall cut it at right angles, and, if it cuts it at right angles, it shall bisect it. Let ABC be a circle; and let CD, a straight line...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...of the circle, and join EF : and because FE, a straight line through the centre, bisects another AC, which does not pass through the centre, it shall cut it at right (3. 3.) angles; wherefore FEA is a right angle. Again, because the straight line FE bisects the straight...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...circumference; therefore it falls within it. Wherefore, if any two points, &c. QED PROP. III. THEOR. If a straight line drawn through the centre of a circle...the centre, it shall cut it at right angles : and if it cut it at right angles, it shall bisect it. Let ABC be a circle; and let CD, a straight line...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1832 - 333 pages
...A and B, therefore AB is within the circle. Wherefore, if any two points, &c. QED PROP. III. THEOR. If a straight line drawn through the centre of a circle bisect a straight line in the circle, which does not pass through the centre, it will cut that line at right angles; and if it...
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