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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 Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - 1867 - 400 páginas
...is that which is half of the given square. 504. Divide a given straight line into two parts so that the squares on the whole line and on one of the parts jnay be together double of the square on the other part. 505. Two rectangles have equal areas and equal...
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Report on the examination for admission to the Royal military academy at ...

...without taking the same three children together more than once. How often will each child go ? 11. If a straight line be divided into any two parts,...part, together with the square on the other part. Where does Euclid afterwards use this proposition? 12. To inscribe a square in a given circle. 13....
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 páginas
...CB, is equal to the square on CD. Wherefore, if a straight line, &c. QED PROPOSITION VII. THEOREM. If a straight line be divided into any two parts, the squares on the whole line, and on one of Uie parts, are equal to twice the rectangle contained by the whole and that part, together with the...
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Papers for the schoolmaster, Volumen4

1868
...line be divided into an; two parts, the squares of the whole line and one of the parti are together equal to twice the rectangle contained by the whole and that part, together with the square of the other part. 3. In an obtuse angled triangle, if a perpendicular be drawn from either of the...
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Report of the commissioners, Volumen6

...line be divided into any two parts : then the squares of the whole line and one of the parts shall be equal to twice the rectangle contained by the whole and that part together with the square of the other part. 4. The square of the difference of two numbers is equal to the sum of the squares...
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The Edinburgh university calendar

Edinburgh univ - 1868
...Parallelograms upon equal bases and between the same parallels are equal. 4. Prove Prop. 47, BI 5. 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 line...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870
...PBOP. 7. — THEOB. If a st. 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 a square of the other part. Cons.— 46. I., Pst. 1 and 31. I. DEM. — 43. I., AM. 2 and 6, Def. 30....
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Elements of geometry, containing the first two (third and fourth ..., Parte1

Euclides - 1871
...Shew that Propositions V. and VI. might be deduced from this Proposition. PROPOSITION VII. THEOREM. If a straight line be divided into any two parts,...that part together with the square on the other part. s Let AB be divided into any two parts in C. Then must sqq. on AB, BC— twice rect. AB, BC together...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - 1872
...fifth proposition the former of these two Qs is the larger, in the sixth, the latter. PBOPOSITION VTI. If a straight line be divided into any two parts,...squares on the whole line and on one of the parts are together equal to twice the rectangle contained by the whole and that part together with the square...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - 1872 - 349 páginas
...for a given parallelogram, can have ? Ii. 11. Divide a given straight line into two parts such that the squares on the whole line and on one of the parts shall be together double of the square on the other part. 1867. in. 22. If the chords, which bisect...
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