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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 synoptical Euclid; being the first four books of Euclid's Elements of ... - Side 97
av Euclides - 1853
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 sider
...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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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 sider
...AE.EC is equal to the rectangle BE.ED. If, therefore, two chords of a circle, &c. PROP. XXXVI. THEOR. IF from any point without a circle two straight lines...the circle, and the part of it without the circle, is equal to the square of the line which touches it. Let D be any point without the circle ABC, and...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 sider
...showing that AE x EC and BE x ED are each = GE x EH, and .'. = each other. PROPOSITION XXXVI. Theorem. If from any point without a circle two straight lines...the circle, and the other touches it, the rectangle B/ contained by the whole line which cuts the circle, and the part of it without the circle, shall...
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A Treatise on Astronomy

L. H. Tyler - 1837
...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 the circle, and the part of it without the circle is equal to the square of the line which touches it, ie the distance cn multipled into nb, equals the...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...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. Let...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...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 meeti shall touch the circle. Let...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...because, as has been shown, AE.EC = GE.EH, and BE.ED=GE.EH; therefore AE.EC=BE. ED. PROP. XXXVI. THEOR. If from any point without a circle two straight lines...the circle, and the part of it without the circle, is equal to the square of the line which touches it. Let D be any point without the circle ABC, and...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...Wherefore, if two straight lines, &c. QED PROP. XXXVI. THEOR. IF from any point on the exterior of a circle two straight lines be drawn, one of which...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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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...proposition and the following. See the Notes at the end of tb" »«i"—•< PROP. XXXVI. THEOR. — If from any point without a circle two straight lines...the circle, and the part of it without the circle, is equal to the square of the line which touches it. Let D be any point without the circle ABC, and...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...circle there be draimi 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 withmit the circle be equal to the square of the line which, meets it, the line which meets shall touch...
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