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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. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 45
by Euclides - 1814
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The First Six Books of the Elements of Euclid, with a Commentary and ...

Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...rectangle under either of them and a third of the other, #c. #c. PROPOSITION II. THEOREM. (223) If a right line (AB) be divided into any two parts (in C), the square of the whole line is equal to the sum of the rectangles under the whole (AB) and each of the parts (AC,...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...-\- b. Multiply this equation by d, then sb = ab + 66, which is the prop. PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square cf the whole line is equal to the squares of the two parts together with twice the rectangle contained...
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The Quarterly Journal of Education, Volume 5

Education - 1833
...equal to the 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,...together, with twice the rectangle contained by the parts. a. Find the value of x in x1 — a x-\-b*^0. b. Divide a*— 3x*+x* + J x'-l'2x + 6 by ^-3. Find the...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1835 - 316 pages
...therefore, multiplying both members of this equality by c, we shall have ac = bc-\-c2. PROP. IV. THEOR. Tf a straight line be divided into any two parts, the...be divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB2=...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 513 pages
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C; the rectangle contained by AB, BC, together with the rectangle * AB, AC, shall be equal...
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The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...the diagonal of any parallelogram, are equal so one another. Which was te be proved. PROP. XX. THEOR. If a straight line be divided into any two parts,...rectangle contained by the parts. Let the straight line AB he divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice...
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The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...equal to the 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,...together with twice the rectangle contained by the parts. Сок. From the demonstration, it is manifest that the parallelograms about the diameter of a square...
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A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 128 pages
...the rectangle under DE and 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...
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The Mechanic's Calculator: Comprehending Principles

William Grier - Mechanical engineering - 1836 - 344 pages
..., 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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The Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - Mechanical engineering - 1836 - 344 pages
...and 9 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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