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" IF a straight line be divided into any two parts, the squares of the whole line, and of one of the parts, are equal to twice the rectangle contained by the whole and that part, together with the square of the other part. "
The synoptical Euclid; being the first four books of Euclid's Elements of ... - Página 53
por Euclides - 1853
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - 513 páginas
...LG: but the gnomon CMG and LG make up the whole figure CEFD, which is the square of CD ; therefore the rectangle AD, DB, together with the square of...the square of CD. Wherefore, if a straight line, &c. Q. £. JO. PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the whole...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - 186 páginas
...into the parts a and b, and x be equal to s, then sx = ax + bx becomes ss = <zs + bs. PROPOSITION III. THEOREM. If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the square of that part together...
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The Elements of Euclid; viz. the first six books, together with the eleventh ...

Euclides - 1834 - 518 páginas
...LG : but the gnomon CMG and LG make up the whole figure CEFD, which is the square of CD ; therefore the rectangle AD, DB, together with the square of...square of CD. Wherefore, if a straight line, &c. QED PROPOSITION VII. THEOR. — If a straight line be divided into any two parts, the squares of the whole...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 páginas
...Cor. 4. 2. rectangle AD, DB : Add to each of these LG, which is equal to the square of CB, therefore the rectangle AD, DB, together with the square of CB, is equal to the gnomon CMG and the figure LG : But the gnomon CMG and LG make up the whole figure CEFD, which is the...
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The Element of Geometry

John Playfair - 1836 - 114 páginas
...equal to the rectangle AD, DB ; add to each of these LG, which is equal to the square of CB ; therefore the rectangle AD DB, together with the square of CB, is equal to the gnomon CMG and the figure LG: but the gnomon CMG and LG make up the whole figure CEFD, which is the...
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Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 páginas
...to the rectangle AD • DB ; add to each of these LG, which is equal to the square of CB ; therefore the rectangle AD • DB, together with the square of CB, is equal to the gnomon CMG, together with LG. But the gnomon CMG, together with LG, makes up the whole figure CEFD,...
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 332 páginas
...produced. Let the straight line AB be bisected in C, and produced to the point D ; the rectangle AD.DB together with the square of CB, is equal to the square of CD. Upon CD describe (Prop. 46.1.) the square CEFD, join DE, and through B draw (Prop. 31. 1.) BHG parallel...
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The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - 1837 - 410 páginas
...equals CB and CA ; therefore NB is equal (I. ax. 2.) to AD. But (II. 5.) the rectangle NB.BD, or AD.BD, together with the square of CB, is equal to the square of CD : which was to be proved. * After it has been proved, as above, that HF is equal to AL, the rest of...
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A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 112 páginas
...Proved by showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*. PROPOSITION IV. Theorem. 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...
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The Elements of Euclid

Euclid - 1838 - 478 páginas
...LG : but the gnomon CMG and LG make up the whole figure CEFD, which is the square of CD ; therefore the rectangle AD, DB, together with the square of...the square of CD. Wherefore, if a straight line, &c. a. ED PROP. VII. THEOR. Ir a straight line be divided into any two parts, the squares of the whole...
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