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" The diameter is the greatest straight line in a circle; and of all others, that which is nearer to the centre is always greater than one more remote; and the greater is nearer to the centre than the less. Let ABCD be a circle, of which... "
Euclid's plane geometry, books iii.-vi., practically applied; or, Gradations ... - Side 31
av Euclides - 1861
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 sider
...straight lines, &c. Q, ED PROP. XV. THEOR. The diameter is the greatest straight line in a cirele ; and of all others• that which is nearer to the centre...the greater is nearer to the centre than the less. Let ABCD be a circle, of which the diameter is AD, and the centre E ; and let BC be nearer to the centre...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...CG ; wherefore AB is equal to CD. Therefore equal straight lines, &c. Q, ED . f± PROP. XV. THEOR. The diameter is the greatest straight line in a circle ; and of all others, that which is nearer to Ike centre is always greater than one more remote ; and the greater is nearer to the centre than the....
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821
...themselves are r= and .-. the given lines ar£ =. PROP. 15: THEOR. The diameter i& the greatest right line in a circle, and of all others that which is nearer to the centre is greater than the more remote. PART 1. The dianieter is greater than any other line. For connect the...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 sider
...CG ; wherefore AB is equal to CD. Therefore equal straight lines, &c. UED Proposition XV. Tlteorem. The diameter is the" greatest straight line in a circle...which is nearer to the centre is always greater than оце more remote ; and the greater is nearer to ;he centre than the less. Let ABCD be a circle of...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1826 - 320 sider
...diameter is the greatest straight line in a eirele ; and of all others, that whieh is nearer to the eentre is always greater than one more remote ; and the greater is nearer to the eentre than the less. Let ABCD be a eirele, of whieh the diameter is AD, and the eentre E; and let...
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Elements of Arithmetic, Algebra, and Geometry

George Lees - 1826
...bisecting lines meet, will be the centre of the circle. Book II. ~~V~"' PROP. II. THEOREM. The diameter AD is the greatest straight line in a circle; and of all others, BC, FG ; BC, which is nearer to the centre, is always greater than FG, the one more remote, and the...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 sider
...to CD. Therefore equal straight lines, &c. QED tHyR. t3Ax. t 6 Ax. SeeN. 1 12. 1. PROP. XV. THEOR. The diameter is the greatest straight line in a circle;...the greater is nearer to the centre than the less. Let ABCD be a circle, of which the diameter is AD, and the centre E; and let BC be nearer to the centre...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 sider
...or the chords AB, CD, are equal (3. 3). Therefore, equal chords &c. QED ED. PROPOSITION XV. THEOREM. The diameter is the greatest straight line in a circle ; and of all other lines that which is nearer to the centre is greater than one more remote ; and the greater line...
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Geometry, Plane, Solid, and Spherical, in Six Books: To which is Added, in ...

Pierce Morton - 1830 - 272 sider
...mutual bisection would be at right angles to each of them, which is absurd. PROP. 4. (Eue. iii. 15.) The diameter is the greatest straight line in a circle; and, of others, that which is nearer to the centre it greater than the more remote : also the greatt-t is nearer...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1832 - 333 sider
...double of CG; wherefore AB is equal to CD. Therefore equal straight lines, &c. QED PROP. XV. THEOR. The diameter is the greatest straight line in a circle;...the greater is nearer to the centre than the less. Let ABCD be a circle, of which the diameter is AD, and the centre E; and let BC be nearer to the centre...
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