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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 ... - Side 53
av Euclides - 1853
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Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...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 CB, is equal to the square of CD. Wherefore, if a straight line, Ac. «,in D. PROP. VII. THEOR. If a straight line be divided into any two parts, the squares of the...
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Euclid, Robert Simson - 1838 - 416 sider
...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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The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 351 sider
...the rectangle AD, DB: add to each of these equals 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 geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...is equivalent to the square of C D. Wherefore, if a straight line, &c. QED РRОР. VII. ТНЕОВ, IF a straight line be divided into any two parts : the squares of the whole line, and one of the parts, are equivalent to twice the rectangle contained by the whole and that part, together...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...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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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...the rectangle AD, DB : add to each of these equals 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 First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...and CA ; therefore NB is equal (I. ax. 2) to AD. NA cap 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. PROP. VII. THEOB. — If a straight line be divided into any two parts, the...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...is equal to the gnomon CMG : To each of these add 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 Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - 1846 - 317 sider
...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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