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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. Let the straight line AB be divided... "
Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ... - Página 53
por Euclides - 1860
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...of CB, is equal to the 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 line, and of one of the parts, are equal to twice the rectangle contained by the whole...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 páginas
...line be divided into any two parts, the squares of the whole line and one of the parts are together equal to twice the rectangle contained by the whole and that part, together with the square of the other part. With the same construction as in (44), and in the same manner it may be shewn, that...
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Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...If a straight line (AB) be divided into any two parts (in C), the squares of the whole lint, and of one of the parts, are equal to twice the rectangle contained by the whole and Hunt part, together with the square of the other part: that is, AB2 + BC2=twice AB'BC + AC!. [See Diagram,...
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Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855
...from D, the middle point of BC, DE is drawn perpendicular to AS: shew that BE is, one-fourth of AB. 5. If a straight line be divided into any two parts, the squares on the whole line and one of the parts, shall be together equal to twice the rectangle contained by the whole line and that...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855
...the rectangle AD.DB, and the square of С В is equal to the square of СD. Р B, O P. VII. THEOREM. 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...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...triangle. 7. 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...the whole and that part, together with the square of the other part. 8. Divide a given straight line into two parts, so that the rectangle contained...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

John Playfair - 1856 - 318 páginas
...VII. THEOR. If a straight line be divided into two parts, the squares of the whole line, and . ^jgfone of the parts, are equal to twice the rectangle contained...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...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...to one anoiher. If one of the complements be a square, the parallelogram will also be a square. 4. 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...
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National Society's Monthly Paper

1856
...anle. . o rag ne o appy a paraeogra have one of its angles equal to a given rectilineal angle. and 2. 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...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...BC and BD together with twice the rectangle BC, BD ; that is (Prop. 49.), to the square of C D. LII. If a straight line be divided into any two parts, the squares of the whole line and of one of the parts is equal to twice the rectangle contained by the whole and...
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