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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 ... - الصفحة 41
بواسطة Euclides - 1816 - عدد الصفحات: 528
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## Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole fine. 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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## Proceedings

...right angles. 3. Parallelograms upon equal bases, and between the same parallels, are equal. 4. If a straight line be divided into any two parts, the...square of the whole line is equal to the squares of each of the parts together with twice the rectangle contained by the parts. 5. Equal straight lines...
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## Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - 1844 - عدد الصفحات: 252
...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...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. •..-••' Let the side of a square...
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## The first six and the eleventh and twelfth books of Euclid's Elements; with ...

James Thomson - 1845 - عدد الصفحات: 358
...to the square of BC, together with the rectangle AC.CB.* If, therefore, &c. PROP. IV. THEOR. — If a straight line be divided into any two parts, the...the squares of the two parts, together with twice their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is...
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## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Robert Potts - 1845
...line is equal to four times the square of half the line. Also, if a line be divided into any three parts, the square of the whole line is equal to the squares of the three parts, and twice the rectangle contained by every two parts. Prop. iv. Algebraically, (fig. Prop,...
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## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - عدد الصفحات: 199
...twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square...
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## A system of practical mathematics; being no.xvi. of a new series of school-books

1845
...two parts in the point C, the proposition becomes the following. If a straight line be divided into two parts, the square of the whole line is equal to the sum of the squares of the parts, together with twice the rectangle contained by the parts. Cor. 2....
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## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...under AC and CF. PROPOSITION IV. THEOREM. If a right line (AB) be divided into any two parts, (in O) the square of the whole line is equal to the squares of the parts, together with twice the rectangle under the parts. On AB describe the square ACDB, and draw...
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## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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 the point C : the rectangle AB, BC shall be equal to the rectangle AC, CB, together with the square...
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## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - عدد الصفحات: 317
...contained by the whole and each of the parts, are together equal to the square of the whole line. c B Let the straight line AB be divided into any two parts in the point C ; the rectangle AB.BC, together with the rectangle AB.AC, is equal to the square of AB...
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