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" ... the product of three alternate segments taken in order is equal to the product of the other three segments. "
The Mathematician - Page 95
1845
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 290 pages
...harmonically. 16. If through any point within or without a triangle, lines be drawn from the angular points to meet the opposite sides, and if lines joining the...of section be produced to meet the sides produced if necessary, the three points of concourse are in one line. 17- If a semicircular and quadrantal arc...
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...harmonically. 28. If through any point within or without a triangle, lines be drawn from the angular points to meet the opposite sides, and if lines joining the...of section be produced to meet the sides produced if necessary, the three points of concourse are in one line. 29. To draw a straight line, so that the...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...angle. 26. If through any point within or without a triangle, lines be drawn from the angular points to meet the opposite sides, and if lines joining the...of section be produced to meet the sides produced if necessary, the three points of concourse are in one line. 27. Describe a rhombus equal to a given...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1892 - 460 pages
...drawn to cut a given system ot lines is called a transversal. 1. If three concurrent straight lines are drawn from the angular points of a triangle to meet the opposite sides, then the product of three alternate segments taken in order is equal to the product of the other three...
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Calendar of the University of Sydney

University of Sydney - 1898 - 548 pages
...angle by a constant amount, find the locus of the vertex. .. ;. ,. 3. If three concurrent arcs are drawn from the angular points of a triangle to meet the opposite, sides, find the relation which holds between the six segments of the angles. Also if a great circle cuts the...
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A Text-book of Euclid's Elements for the Use of Schools, Book 1

Euclid - Euclid's Elements - 1904 - 488 pages
...drawn to cut a given system of lines is called a transversal. 1. If three concurrent straight lines are drawn from the angular points of a triangle to meet the opposite sides, then the product of three alternate segments taken in order is equal to the product of the othe,r three...
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Journal of Education

Education - 1911 - 1334 pages
...trihedral angle, any two are together greater than the third. * 8. If three concurrent straight lines are drawn from, the angular points of a triangle to meet the opposite sides, then the product of three alternate segments taken ii> order is equal to the product of the other three...
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The Calendar

University of South Africa - Universities and colleges - 1913 - 768 pages
...segments is equal to the product of the other three segments. If three concurrent straight lines are drawn from the angular points of a triangle to meet the opposite sides, then the product of three alternate segments taken in order is equal to the product of the other three...
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The Bombay University Calendar, Volume 1

University of Bombay - 1912 - 1228 pages
...sides about the equal angles. Concurrency and Collinearity. If thre<? eon"irrrent stmight lines are drawn from the angular points of a triangle to meet the opposite sides, the product of three alternate segments taken in order is equal to the product of the other throe segment*....
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mathematical problem papers

228 pages
...properа tional between v1 and г>3. 2—2 1. Straight lines AD, BE, С F which meet in a point P are drawn from the angular points of a triangle to meet the opposite sides in D, E, /''respectively. Prove that the straight lines joining А, В, С to the middle points of...
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