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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. "
A System of Popular Geometry: Containing in a Few Lessons So Much of the ... - Página xxxi
por George Darley - 1836 - 128 páginas
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1827 - 332 páginas
...than in ordinary language. The proposition, (Euc. 4- 2.) that when a straight line is divided into two parts, the Square of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonstrated, by involving...
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - 1828 - 542 páginas
...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 - 1829 - 186 páginas
...rectangle contained by 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 Quarterly Journal of Education, Volumen5

1833
...rectangle contained by the 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 First Six Books of the Elements of Euclid: With Notes

Euclid - 1833 - 183 páginas
...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 Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 páginas
...with the square of BC. " 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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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

1836 - 472 páginas
...rectangle contained by the 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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The Element of Geometry

John Playfair - 1836 - 114 páginas
...parallelogram, are 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 Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - 1836 - 344 páginas
...BC Al) and EF, and AD and FB: thus expressed, AD. AB = AD . AE+ AD . EF + AD . FB.* If a right line be divided into any two parts, the square of the whole line, is equal to both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any...
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The Mechanic's Calculator: Comprehending Principles

William Grier - 1836 - 344 páginas
...and AD and EF, and AD and FB: thus expressed, AD . AB = AD . AE + AD . EF + AD . FB.* If a right line be divided into any two parts, the square of the whole line, is equal to both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any...
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