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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 - 1833 - 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...nearer to the centre is always greater than one more r&mote ; and the greater is nearer to the centre than the less. Let ABCD be a circle, oC which the...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 183 sider
...are also equal (8). PROP. XV. THEOR. The diameter is the greatest right line in a circle : Pig 22. and of all others that which is nearer to the centre is See N. greater than the more remote. Part. 1 . The diameter AB is greater than any other line ED. For...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...diameter is the greatest straight line in a circle; See N. and, of all others, that which is nearer to ike centre is always greater than one more remote ; and the greater is • to the centre than the less. Let ABCD be a circle, of which the diameter is AD, and the centre...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 sider
...: wherefore AB is equal to CD. Therefore, « equal straight lines," &c. QED PROP. XV. THEOH. See N. The diameter is the greatest straight line in a circle : and, of all of hers, that which is nearer to the centre is always greater than one more remote / and the greater...
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...(i) Every diameter divides the circle and its circumference into two equal parts . . n ote 78 (с) The diameter is the greatest straight line in a circle; and, of others, that which is nearer to the centre is greater than the more remote ; also, the greater is nearer...
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The Element of Geometry

John Playfair - 1836 - 114 sider
...double of CG; wherefore AB is equal to CD. Therefore, equal straight lines, &c. QED PROP. VII. 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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...from the centre ; and those which are equally distant from the centre are equal to one another. XV. The diameter is the greatest straight line in a circle ; and of all others, that which is nearest the centre is always greater than the more remote; and the greater is nearer to the centre...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 sider
...to CG : But AB is double of AF, and CD double of CG ; wherefore AB is equal to CD. 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 Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 sider
...A + B = C -f D ; then,if A = C, B=D; or PROPOSITION XV. THEOREM. The diameter is the greatest chord in a circle ; and of all others, that which is nearer...the greater is nearer to the centre than the less. Let ABCD he a circle, of which the diameter is AD, and the centre E ; and let BC be nearer to the centre...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...Demonstration to Part 2nd. 1. Prove that AF* = CG*, and .'. AF = CG, 2. that AB = CD. PROPOSITION XV. Theorem. The diameter is the greatest straight line in a circle...which is nearer to the centre is always greater than the more remote; and conversely, the greater is nearer to the centre than the less. Part 1st. That...
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