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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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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1833 - 333 Seiten
...straight lines, on» of which cuts the circle, and the other meets it ; if the rectangle eon* tained by the whole line, which cuts the circle, and the part of it with* out the circle,*be equal to the square of the line which meets it, the line which meets shall...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 Seiten
...other meets the circle, ' and that 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 " 37. 3. of BD which meets it,, the straight line BD touches * the circle ACD : and because BD touches...
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The Elements of Euclid: viz. the first six books, together with the eleventh ...

Robert Simson - 1835 - 513 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...equal to the square of the line which touches it. Let D be any point without the circle ABC, and DCA, DB two straight lines drawn from it, of which DCA...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1835 - 316 Seiten
...AE.EC=BE.ED. PROP. XXXII. 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...without the circle, is equal to the square of the line whith touches it. Let D be any point without the circle ABC, and DCA, DB two straight lines drawn from...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 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 contained by the whole line which cuts tJie circle, and the part of it without the circle, is equal to the square of the line which touches...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - 542 Seiten
...If from any point, without the circumference of 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, and the part of that line without the circle, is equal to the square of the line which touches. The...
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Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - 1836 - 524 Seiten
...If from any point, without the circumference of 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, and the part of that line without the circle, is equal to the square of the line which touches. The...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 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 a circle, be equal to the line which meets it, the line which meets shall touch the circle. BOOK iv....
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A Treatise on Astronomy

L. H. Tyler - 1837 - 302 Seiten
...less is the polar than the equatorial di ameter ? What is the curvature of the earth for one mile ? rectangle* contained by the whole line which cuts...equal to the square of the line which touches it, ie the distance cn multipled into nb, equals the square of a b : Now the square of ab, or one mile,...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 112 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. Steps...
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