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" When it is affirmed (for instance) that " if two straight lines in a circle intersect each other, the rectangle contained by the segments of the one is equal to the rectangle contained by the segments of the other... "
Elementary Plane Geometry: Inductive and Deductive - Página 95
por Alfred Baker - 1903 - 144 páginas
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Vectors and Rotors: With Applications

Olaus Henrici, George Charles Turner - 1903 - 236 páginas
...coincides with AiA and the theorem follows at once. (3) If two straight lines intersect within or without a circle, the rectangle contained by the segments of...rectangle contained by the segments of the other. Let AB, CD be the lines intersecting at P and let O be the centre of the circle. If PA = a, PB=ta,...
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Elementary Geometry: Practical and Theoretical

Charles Godfrey, Arthur Warry Siddons - 1903 - 384 páginas
...substantially those of Euclid. = ar — y2. Pythagoras EUCLID in. 35, 36. If two chords of a circle intersect, the rectangle contained by the segments of the one...rectangle contained by the segments of the other. CASE I. Let the chords AB, CD intersect at P, a point inside the circle. To prove that rect. PA . PB...
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Report of the Committee of Council on Education in Scotland

Great Britain. Scottish Education Department - 1903 - 964 páginas
...that they arc equal in area. A 4. It two chords of a circle intersect within the circle, prove that the rectangle contained by the segments of the one...rectangle contained by the segments of the other. Ali, CI) are chords of a circle which intersect in 0 : if АО be | inch, ОП 1-J- inch, CO \ inch,...
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A Text-book of Euclid's Elements for the Use of Schools, Libro 1

Euclid - 1904 - 488 páginas
...PROPOSITIONS 16 AND 17. 1. Apply Proposition 16 to prove that if two chords of a circle intersect, the rectangle contained by the segments of the one...rectangle contained by the segments of the other. 2. Prove that the rectangle contained by the sides of a rightangled triangle is equal to the rectangle...
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Calendar

University of Sheffield - 1905 - 574 páginas
...the one which has the greatest area is a square. C. Prove that if two chords of a circle intersect, the rectangle contained by the segments of the one is equal to that contained by the segments of the other. AB is a diameter of a circle, and AP, BQ are two chords...
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Annual Report - Dept. of Education

Saskatchewan. Department of Education - 1906 - 188 páginas
...arcs. (d) How will the result be changed in (c) if the two chords intersect without the circle? 6. (a) If two chords of a circle cut one another within the...rectangle contained by the segments of the other. III. 35. (6) Enunciate and prove this proposition when extended to n chords and intersecting on the...
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Calendar of the University of Sydney

University of Sydney - 1906 - 738 páginas
...angles. H. Prove that, if two chords of a circle, neither of which passes through the centre, intersect within the circle, the rectangle contained by the...rectangle contained by the segments of the other. If the radius of the circle is 5 inches and the chord is drawn through a point distant 8 inches from...
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Books 3-9

Euclid - 1908 - 456 páginas
...to draw a diameter of the circle. PROPOSITION 35. If in a circle two straight lines cut one another, the rectangle contained by the segments of the one...rectangle contained by the segments of the other. For in the circle ABCD let the two straight lines AC, BD cut one another at the point E ; I say that...
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A Manual of Practical Mathematics

Frank Castle - 1908 - 616 páginas
...circle, such as AC and BD, cut one another at a point £!, the rectangle contained by the segments of one is equal to the rectangle contained by the segments of the other, ie AE.EC=DE.EB. If one line such as AC passes through the centre of the circle and the other is perpendicular...
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The Ontario High School Geometry: Theoretical

Alexander H. McDougall - 1910 - 316 páginas
...IV — 15) If two straight lines cut each other so that the rectangle contained by the segments of one is equal to the rectangle contained by the segments of the other, the four extremities of the two straight lines are concyclic. Hypothesis — The st. lines AB, CD cut...
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