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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 ... - Side 39
av Euclides - 1834
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Elements of Geometry and Conic Sections

Elias Loomis - 1849 - 226 sider
...equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts. Let the straight line AB be divided into any two parts in C; the square on AB is equivalent to the squares on AC, CB, together with twice the rectangle contained...
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Papers for the Schoolmaster

1852
...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,...parts, together with the square of the aforesaid part. following sentence, shewing the variou» clauses, &c. :— " Not to do your best when you are told...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...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,...aforesaid part. Let the straight line AB be divided into two parts in the point C; the rectangle AB, BC is equal to the rectangle AC, CB, together with the...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...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
...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 - 1853 - 147 sider
...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. A New Text ..., Bok 1

Euclides - 1853
...the other part shall be equal to the square of the line which is made up of the whole line and that part. Let the straight line AB be divided into any two parts AC, CB in c. Then four times the rectangle AB, BC together with the square of AC shall be equal to...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...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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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1855 - 318 sider
...rectangle contained by tht whole ami one of the parts, is equal to the rectangle contained by the tw» 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.BC is equal to the rectangle AC.BC, together with BC 2...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...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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