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" If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
Elements of Plane Geometry - Page 64
by Thomas Hunter - 1878 - 132 pages
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...of BC. If therefore a straight line, &c. QED PROP. IV. THEOK. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 544 pages
...double rectangle under every distinct pair of them. Thus if it be divided into three parts x, y, z, the square of the whole line is equal to the sum of the squares of x, y, and z together with twice the sum of the rectangles x X y, y X , and x X x. PROPOSITION...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 210 pages
...the two parts together with the square of the foresaid part. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts together with twice the rectangle contained by the two parts. Or, in other...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1833 - 304 pages
...parallelogram on the same base and of the same altitude. PROP. 2. THEOR. If a right line be divided into any two* parts, the square of the whole line is equal to the sum of the rectangles under the whole line and each of the parts. Describe on the given line an2 (prop. 46, 1.), and through...
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The First Six Books of the Elements of Euclid: With Notes

Euclid - Euclid's Elements - 1833 - 216 pages
...under AC and CB. PROP. IV. THEOR. If a right line (AB) be divided into any two parts Fig. 6. (in 0), the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle under the parts. On AB describe the square ACDB ; draw...
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The Quarterly Journal of Education, Volume 5

Education - 1833 - 412 pages
...two parts together with the square of the aforesaid part. 5. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts together, with twice the rectangle contained by the parts. a. Find the value...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
..." If, therefore, a straight line," &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 172 pages
...CB, that is, the rectangle under AC and CB. This, &c. ART. 92. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts together with twice the rectangle under the parts. Let AB he a right line divided...
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The Element of Geometry

John Playfair - Geometry - 1836 - 148 pages
...equal so one another. Which was te be proved. PROP. XX. THEOR. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Сок. From the...
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