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" If there be two straight lines, one of which is divided into any number of parts, the rectangle contained by the two straight lines is equal to the rectangles contained by the undivided line, and the several parts of the divided line. Let... "
The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ... - Page 40
by Robert Simson - 1827 - 513 pages
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - Geometry - 1810 - 518 pages
...the rectangles contained by the undivided tine, and the parts of the divided line. K H Book H. Lijt A and BC be two straight lines; and let BC be divided ILJ~V~«_I into any parts in the points D, E ; the rectangle contained by the straight lines A, BC...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volume 5

John Mason Good - 1813
...straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained...undivided line, and the several parts of the divided line. Prop. II. Theor. If a straight line be divided înto any two parts, the rectangles contained by the...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1814
...parts of the divided line. Boox II. Let A and EC be two straight lines ; and let BC be di**~v~^ vided into any parts in the points D, E ; the rectangle contained by the straight lines A, TO DEC •1i.i. From the point B draw a G BC is equal to the rectangle contained by A,BD, together...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 pages
...straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is equal to the rectangles contained...undivided line, and the several parts of the divided line. BouK II. Let A and BC be two straight lines ; and let BC be di-^ " vided into any parts in the points...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...straight lines, one of which is divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles' contained...into any parts in the points D, E ; the rectangle A.BC is equal to the several rectangles A.BD, A.DE, A.EC. From the point B draw (11. 1.) BF at right...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...straight lines, one of which is divided into any number of parts ; the rectangle contained by the two straight lines is equal to the rectangles contained...undivided line, and the several parts of the divided line. • */ -i Let A and BC be two straight lines ; and let BC be divided into any parts in the points D,...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid, Robert Simson - Geometry - 1821 - 516 pages
...straight lines, one of which is divided into any number of parts; the rectangle contained by the two straight lines, is, equal to the rectangles contained...parts in the points D, E; the rectangle contained by * G the straight lines A, BC is equal to B the rectangle contained by A, BD, together with that contained...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...straight lines, one of which is divided into any number of parts ; the rectangle contained by the two straight lines, is equal to the rectangles contained...the rectangle contained by the straight lines A, BC is equal to the rectangle contained by A, BD, together with that contained by A, DE, and that contained...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 320 pages
...straight lines is equal to the reetangles eontained by the undivided line, and the several partsof the divided line. Let A and BC be two straight lines...be divided into any parts in the points D, E ; the reetangle A.BC is equal to the several reetangles A.BD, A.DE, A.EC. From the point B draw (11.1.) BF...
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Elements of Geometry: With Notes

John Radford Young - Euclid's Elements - 1827 - 208 pages
...PROPOSITION IV. THEOREM. If there be two straight lines of which one is divided into parts, the sum of the rectangles contained by the undivided line, and the several parts of the other, will be equal to the rectangle contained by the two whole lines. Let the lines be AB, AC, of...
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