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" Wherefore from the given circle ABC has been cut off the segment BAC, containing an angle equal to the given angle DQEP PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Page 83
by Euclides - 1816 - 528 pages
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834
...be done. PROPOSITION XXXV. THEOR. — If two straight lines cut one another within a circle, See N. the rectangle contained by the segments of one of...segments of the other. Let the two straight lines AC, BD cut one another in the point E, within the circle ABCD : the rectangle contained by AE, EC, shall be...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...Which was to be done. PROP. XXXV. THEOR. If two straight lines within a circle cut one another, See N. the rectangle contained by the segments of one of...Let the two straight lines AC, BD within the circle A BCD, cut one another in the point E : the rectangle contained by AE, EC is equal to the rectangle...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...the alternate segments of the circle. XXXIV. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. XXXVI. If from any point without a circle two straight lines be drawn, one of which cuts the circle,...
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Solutions of the Cambridge Problems, from 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1836
...of section. 3. If two straight lines within a circle cut one another, the rectangle contained Ъу the segments of one of them is equal to the rectangle contained by the segments of the other. 4. Inscribe an equilateral and equiangular hexagon in a given circle. 5. If any number of magnitudes...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1836 - 471 pages
...angle D. Which was to be done.PROP. XXXV. THEOR. If two straight lines within a circle cut one another, the rectangle contained by the segments of one of them is equal to the rectangle contained by me segments of the other. Let the two straight lines AC, BD, within the circle ABCD, cut one another...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - Euclid's Elements - 1837 - 88 pages
...alternate segment BJC ~ ZD PROPOSITION XXXV. Theorem. If two straight lines within a circle cut each other, the rectangle contained by the segments of...rectangle contained by the segments of the other. • In case 1st, E is the centre of the 0, and evident that AE x EC = BE x ED. it is Steps of the Demonstration...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 390 pages
...; that is, the difference between it and a right angle. IF two chords of a circle cut one another, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. In the circle ABCD, let the two chords AC, BD cut one another in the point E : the rectangle AE.EC...
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A Treatise on Mensuration for the Use of Schools

Commissioners of National Education in Ireland - 1837
...-36571 ; hence 30-24 + -36571 = 30-60571 the area. Note. If two chords of a circle cut one another, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. This is the 35th Proposition of the IIL Book of Euclid. 4. Required the area of the segment AGFB whose...
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...angle equal to the given angle D. PROPOSITION XXXV. THEOREM. If two chords in a circle cut one another, the rectangle contained by the segments of one of...rectangle contained by the segments of the other. If AC, BD, pass each of them through the centre, so that E is the centre; it is evident that AE, EC,...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...D. Which was to be done. PROP. XXXV. THEOR. If two straight lines cut one another within a circle, the rectangle contained by the segments of one of...segments of the other. Let the two straight lines AC, BD, cut one another In the point E within the circle ABCD: the rectangle contained by AE, EC shall be equal...
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