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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 geometry of the three first books of Euclid, by direct proof from ... - Seite 80
von Euclides - 1856
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 410 Seiten
...circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; 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 the circle touches it. If from...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 332 Seiten
...and the other meets the circle, and the rectangle AB.BC contained by the whole of the cutting line, and the part of it without the circle, is equal to the square of BD, which meets it ; the straight line BD touches (37. 3.) the circle ACD. And because BD touches the...
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Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 246 Seiten
...tangent and the other cuts the circle, the rectangle contained by the line which cuts the circle and by the part of it without the circle is equal to the square of the tangent. 11. If, from the same point without a circle, several straight lines are drawn cutting the...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 Seiten
...cuts, and the other meets, the circle, and that the rectangle I AB • BC contained by the secant, and the < part of it without the circle, is equal to the square of BD which meets it ; the straight line BD touches the circle ACD fi" (III. 37) ; and because BD touches...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 Seiten
...&c. PROP. XXXVI. THEOR. If from any point without a circle two straight tines be drawn, one of which cuts the circle, and the other touches it; the rectangle...the circle, and the part of it without the circle, shall be equal to the square of the line which touches it. Let D be any point without the circle ABC,...
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An Essay on the Use of the Spirit Level: As Applied to Engineering and Other ...

Thomas Oswald Blackett - 1838 - 106 Seiten
...36, 3dBook EuclidJ. " 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...the circle, and the part of it without the circle, shall be equal to the square of the line which touches it-" Let D be any point without the circle ABC,...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1838 - 434 Seiten
...QED PROP. XXXVI. THEOR. 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...the circle, and the part of it without the circle, shall be equal to the square of the line which touches it. Let D be any point without the circle ABC,...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 Seiten
...QED PROP. XXXVI. THEOR. If from any point without a circle two straight lints be drawn, one of which cuts the circle, and the other touches it; the rectangle...the circle, and the part of it without the circle, shall be equal to the square of the line which touches it. Let D be any point without the circle ABC,...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...XXXVI. THEOR. IF from any point on the exterior of a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle...whole line which cuts the circle, and the part of it which is on the exterior of the circle, shall be equivalent to the square of the line which touches...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 332 Seiten
...circle there be drawn two straight lines, one of which cuts the circle, and the other meets it ; 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. Let...
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