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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 ... - Seite 53
von Euclides - 1853
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1806 - 518 Seiten
...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 : buf 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 ...

Euclid - 1810 - 518 Seiten
...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...to the square of CD. Wherefore, if a straight line, 8cc. QED PROP. 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 ...

Euclides - 1814 - 558 Seiten
...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...Wherefore, if a straight line, &c. QED PROP. VII. THEOR. IF a straight line be divided into any two parts, the squares of the whole line, and of one...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 Seiten
....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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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Band 5

John Mason Good - 1819 - 740 Seiten
...square of the straight line which is made up of the half and. the part produced. Prop. VII. Theor. If a straight line be divided into any two parts, the squares of the whole line, ajid of one of the parts, are equal 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 - 1819 - 317 Seiten
...Let the straight line AB be bisected in C, and produced to the point A B k) ; the rectangle AD.DB, together with the square of CB, is equal to the square of CD. Upon CD describe (46. 1.) the square CEFDJoin DE, and through B draw (31. 1 .) BHG parallel to CE or...
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The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ...

Euclides - 1821 - 294 Seiten
...together with the D 5 of the line drawn to base is = to the square of the side. PROP. 7, THEOR. Mf a right line be divided into any two parts, the squares of the whole line and either segment are: equal to double the rectangle under the whole line and that segment, together with...
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Euclid's Elements of Geometry: The Six First Books. To which are Added ...

Rev. John Allen - 1822 - 516 Seiten
...rectangle ZBD being equal to the rectangle ADB, because ZA is equal to BD and ZB to AD, the rectangle ADB with the square of CB, is equal to the square of CD. Scholium. — A like observation, as is made in the scholium to prop. 3 of this book, is applicable...
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The First Six Books with Notes

Euclid - 1822 - 179 Seiten
...to the base, equal to the square of the side (2). PROP. VII. THEOR. * Fig. is. If a right line (AB) be divided into any two parts, the squares of the whole line ( AB) and either segment (CB) are together equal to double the rectangle under the whole and that segment,...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - 372 Seiten
...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...
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