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" If from a point without a 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... "
Elements of Arithmetic, Algebra, and Geometry - Page 164
by George Lees - 1826
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 552 pages
...touches the circle. PROP. XXXVII. THEO R. IF from a point without a circle there be drawn two ftraight lines, one of which cuts the circle, and the other meets it ; if the re&anglc contained by the whole line which cuts the circle, and the part of it without the circle be...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

Euclid, John Playfair - Euclid's Elements - 1795 - 462 pages
...touches the circle. PROP. XXXVII. THEO R. IF from a point without a circle there be drawn two ftraight lines, one of which cuts the circle, and the other meets it ; if the reftangle contained by the whole line which cuts the circle, and the part of it without the circle...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - Trigonometry - 1799 - 374 pages
...touches the circle. PROP. XXXVII. THEOR. IF from a point without a circle there be drawn two ftraight lines, one of which cuts the circle, and the other meets it ; if the redlangle contained by the whole line which cuts the circle, and the part of it without the circle...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Mathematics - 1806 - 320 pages
...equal to the square of the straight line AD which touches the circle. Book nt. PROP. XXXVII. THEOR. IF from a point without a circle there be drawn two...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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...same manner it may be shewn that the squares of GH and GI are together equal to the square of OB. (7.) If from a point without a circle there be drawn two straight lines, one of which is perpendicular to a diameter, and the other cuts the circle ; the square of the perpendicular is...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...same manner it may be shewn that the squares of GH and GI are together equal to the square of OB. (7.) If from a point without a circle there be drawn two straight lines, one of which is perpendicular to a diameter, and the other cuts the circle ; the square of the perpendicular is...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Geometry - 1821 - 898 pages
...the squares of the segments of them are together equal lo the square of the diameter. 13. If from * point without a circle there be drawn two straight lines, one of which touches the circle and the other cuts it, and from the point of contact a perpendicular be drawn to...
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A Supplement to the Elements of Euclid

Daniel Cresswell - Euclid's Elements - 1825 - 616 pages
...chord produced meets the quadrantal arch, from the other radius. LIX. TH. If the angle contained by two straight lines, one of which cuts the circle and the other meets it, be equal to the angle in the alternate segment of the circle, the straight line which meets, shall...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 1046 pages
...is equal to the square of the straight 1'ne AD which touches the circle. Proposition XXXVIL Theorem. If from a point without a circle there be drawn two straight lineĢ one of which cuts the circle, and the other meets it j if the rectangle contained by the whole...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Euclid's Elements - 1827 - 462 pages
...circumference ; the squares of the segments of them are together equal to the square of the diameter. 13. If from a point without a circle there be drawn two straight Hues, one of which touches the circle and the other cuts it, and from the point of contact a perpendicular...
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