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" If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. "
The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... - Page 49
by Euclid, Robert Simson - 1829 - 516 pages
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Papers for the Schoolmaster, Volume 2

1852 - 316 pages
...the right angle, is equal to the squares described upon the sides which contain the right angle. III. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. following sentence, shewing the variou» clauses, &c. :— " Not to do your best when...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...equal to the two numbers multiplied together.] 90 BOOK II. • xlvi. 1. THE ELEMENTS PROP. III. THEOR. If a straight line be divided into any two parts,...by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into two parts in the point C; the rectangle AB,...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...AB, BC, is equal to the square of AB. If therefore a straight line, etc. QED PROPOSITION III. THEOR. If a straight line be divided into any two parts,...the rectangle contained by the two parts, together loith the square of the aforesaid part. Let the straight line AB be divided into any two parts in the...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...AB, BC, is equal to the square of AB. If, therefore, a straight line, &c. QED PROP. III. — THEOREM. If a straight line be divided into any two parts,...the rectangle contained by the two parts, together mill the square of the aforesaid part. Let the straight line AB be divided into any two parts in the...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 176 pages
...the square of ab. If QED df therefore a straight line, &c. PROPOSITION III. — THEOREM. If a slraigM line be divided into any two parts, the rectangle...rectangle contained by the two parts, together with tlie square of the aforesaid part. LET the straight line ab be divided into any two parts in the point...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...into any two parts : then the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in c. Then. the rectangle AB,...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...PROPOSITION III.— ТНЕОЕБИ. . ., If a straight line (AB) be divided into any two parts (AC, CB), the rectangle contained ,by the whole and one of the parts is equal to the rectangle contained by the twoparts% together with the square of the aforesaid part : that is, AB-BC = AOCB + :вс«. . ....
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 270 pages
...lines mentioned in its enunciation are equal, their rectangle is в square. PROP. III. THEO КЕМ. If a straight line be divided into any two parts, the rectangle contained by the inhale and one of the parts is equal to the rectangle contained by the two parts, together toith the...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - Euclid's Elements - 1855 - 340 pages
...PROP. III. THEOR. If a straight line be divided into any two parts, the rectangle contained by ttie whole and one of the parts, is equal to the rectangle contained by the twtt parts, together with the square of the aforesaid part. Let the straight line AB be divided...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...and each of the parts. Cor. 2. — In like manner making A equal to one of the parts, it appears that if a straight line be divided into any two parts,...contained by the two parts together with the square of the first mentioned part. XLIX.— EUCLID II. 4. If a straight line be divided into any two parts the square...
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