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" If from any point without a circle two straight lines be drawn, one of -which cuts the circle, and the other touches it; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square... "
The first three books of Euclid's Elements of geometry, with theorems and ... - Page 82
by Euclid, Thomas Tate - 1849 - 108 pages
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Woolwich Mathematical Papers for Admission Into the Royal Military Academy ...

E. J. Brooksmith - Mathematics - 1889 - 356 pages
...produced such that QP= QB, prove that P will lie on an arc of a fixed circle passing through A and B. 7. If from any point without a circle two straight lines be drawn, one of which cuts the circle but does not pass through the centre, and the other touches it : the rectangle contained by the whole...
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Practical Plane Geometry: Giving the Simplest Modes of Constructing Figures ...

John Fry Heather - Geometry, Modern - 1890 - 252 pages
...circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; and if the rectangle contained by the whole line which cuts...the circle, and the part of it without the circle, be equal to the square of the line which meets it, the line which meets shall touch the circle. (Eu....
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1890 - 530 pages
...circle shall be equal to the angles which are in the alternate segments of the circle. 4. If from n point without a circle two straight lines be drawn, one of which cuts the circle (but does not pass through the centre), and the other touches the circle, the rectangle contained by...
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The Harpur Euclid: An Edition of Euclid's Elements

Edward Mann Langley, W. Seys Phillips - 1890 - 538 pages
...of which cuts the circle and the other meets it ; if the rectangle contained by the whole straight line which cuts the circle and the part of it without the circle be equal to the square of the line which meets the circle, the line which meets the circle shall touch...
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Euclid Revised: Containing the Essentials of the Elements of Plane Geometry ...

Euclid - Geometry - 1890 - 442 pages
...the Addenda. Proposition 36. THEOREM — If from any point outside a circle, two straight lines are drawn, one of which cuts the circle and the other touches it ; then the rectangle contained by the whole line which cuts the circle, and the part of it without...
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Sandhurst Mathematical Papers for Admission Into the Royal Military College ...

Royal Military College, Sandhurst - Mathematics - 1890 - 144 pages
...one another, and shall have those angles equal which are opposite to the homologous sides. If from a point without a circle two straight lines be drawn, one of which touches, and the other cuts the circle ; a line drawn from the same point in any direction equal to...
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Examinations Papers

1891 - 718 pages
...the least and PQ the greatest line that can be drawn from P to the circle. D. If from a point outside a circle two straight lines be drawn, one of which...whole line which cuts the circle and the part of it outside the circle is equal to the square on the line which touches it. ENGLISH. The Board of Examiners....
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Report of the Secretary for Public Instruction ...

Queensland. Department of Public Instruction - Education - 1892 - 508 pages
...between that straight line and the circumference, so as not to cut the circle. 'J. If from any |toint without a circle two straight lines be drawn, one...and the other touches it, the rectangle contained liy the segments of the secant shall be equal to the square on the tangent. [Prove this in the case...
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Report of the Council of Public Instruction of the North-West Territories of ...

Northwest Territories Council of Public Instruction - 1897 - 628 pages
...reasons for your answer. (c) Draw a common tangent to two given circles. 5. (a) Prove that if from a point without a circle two straight lines be drawn, one of which cuts the circle, and the other meets it, and if the rectangle contained by the secant and its external segment be equal to the square...
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Report of the Department of Education for the Year ...

Manitoba. Department of Education - Education - 1900 - 582 pages
...circle described on any two sides of a triangle as diameters intersect on the third side. 8. If from a point without a circle two straight lines be drawn,...it, the rectangle contained by the whole line which cute the circles and the part of it without the circle shall be equal to the square on the line which...
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