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" If a chord of a circle is divided into two segments by a point in the chord or in the chord produced, the rectangle contained by these segments is equal to the difference of the squares on the radius and on the line joining the given point with the centre... "
Mathematical Questions and Solutions - Page 19
1869
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Mathematical Questions and Solutions, from the "Educational Times ..., Volume 11

W. J. C. Miller - Mathematics - 1869 - 122 pages
...radius of curvature (VP). [Mr. WHITE states that the main part of this proof is due to Mr. CBOFTON.] From this a simple method of finding a point on the...from it to the circle ; the intersection of these perpendicnlars is a point on the second involute which hns its apse midway between the cnsp of the...
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Syllabus of Plane Geometry: (corresponding to Euclid, Books I-VI) ...

Association for the improvement of geometrical teaching - Geometry, Modern - 1876 - 66 pages
...rectangle contained by these segments is equal to the difference of the squares on the radius and on the line joining the given point with the centre of the circle. COR. i. The rectangle contained by the segments of any chord passing through a given point is the same,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry - 1876 - 446 pages
...rectangle contained by these segments will be equal to the difference of the squares on the radius and on the line joining the given point with the centre of the circle. What propositions in Euclid follow immediately from this ? % (6) Describe a circle which shall pass...
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Elementary geometry

James Maurice Wilson - 1878 - 450 pages
...rectangle contained by these segments is equal to the difference of the squares on the radius and on the line joining the given point with the centre of the circle. Part. En. Let A be a point and CEB a circle, whose centre is O. Then the rectangle contained by the...
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Syllabus of plane geometry, books 1-3, corresponding to Euclid, books 1-4 ...

Mathematical association - 1883 - 86 pages
...rectangle contained by these segments is equal to the difference of the squares on the radius and on the line joining the given point with the centre of the circle. COR. 1. The rectangle contained by the segments of any chord passing through a given point is the same,...
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Examinations Papers

1887 - 644 pages
...rectangle contained by these segments is equal to the difference of the squares on the radius and on the line joining the given point with the centre of the circle. If two straight lines AB, CD cut one another internally or externally at O, so that the rectangle OA,...
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The Elements of Plane Geometry:pPart I(corresponding to Euclid Books I.-II ...

Association for the Improvement of Geometrical Teaching - Euclid's Elements - 1888 - 208 pages
...rectangle contained by these segments ia equal to the difference of the squares on the radius and on the. line joining the given point with the centre of the circle. Let BC a chord of a circle whose centre is O be. divided into two segments at the point A : then shall...
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