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" If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made... "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 83
by Euclides - 1871
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Elements of Plane Geometry According to Euclid

Andrew Bell - Euclid's Elements - 1837 - 240 pages
...DB ; therefore the squares of AD, DB, are double of the squares of AC, CD. PROPOSITION X. THEOREM. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double...
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...unequal lines AC, CD, is equal to the rectangle contained by their sum and difference. PROP. VI. THEOR. If a straight line be bisected, and produced to any...the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half...
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The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...squares of half the line, and of the part intermediate between the points of section. PROP. X. THEOR. If a straight line be bisected, and produced to any point, the squares of the whole produced line, and of the produced part, are together double of the squares of...
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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...AD, DB are double of the squares of AC, CD. Therefore, if a straight line, &c. a ED PROP. X. THEOR. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 320 pages
...are equivalent to double the squares of AC, CD. If therefore a straight line, &c. QED PROP. X. THEOR. IF a straight line be bisected, and produced to any point • the square of the whole line thus produced, and the square of the part of it produced, are together equivalent...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...algebraical expression, where a denotes AC, and b denotes CD ; hence, a+i =AD, a— i=DB. PROP. X. THEOR. b If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...are double of the squares of AC, CD. If therefore a straight line, &c. QED PROPOSITION X. THEOB. — If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 380 pages
...these equals together, and from the suras take 2 AC.CD : then '=2 A(J2-(-2 CD2. PROP. X. THEOR. — If a straight line be bisected, and produced to any point, the squares of the whole line thus produced, and of the part of it produced, are together double of the...
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 544 pages
...of the squares of AC, CD. If therefore a straight line be divided, &c. QED PROPOSITION X. THEOREM. If a straight line be bisected, and produced to any point, the square of the whole line thus produced, and the square of the part of it produced, are together double...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 332 pages
...CD2=(AC+CD) (AC — " CD)." SCHOLIUM. X / it M r"3> ' '•• * PROP. VI THEOR. Ifastraightlinebe bisected, and produced to any point ; the rectangle...the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made up of the half...
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