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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 of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1876 - 403 sider
...opposite angle, and acute angle. (Take the case where the perpendicular falls within the triangle.) 5. If a straight line be divided into any two parts, the squares on the whole line, and one of the parts, are equal to twice the rectangle contained by the whole and...
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major - 1876
...the triangle CNK equal to the triangle ARC, and the triangle BMF equal to the triangle ARB, &c.) 2. If a straight line be divided into any two parts, the squares ou the whole line and one of the parts are equal to twice the rectangle contained by the whole and...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 sider
...on EC, together with the rectangle AC, CB. Therefore, if a straight line, &c. QED Proposition 4.— Theorem. If a straight line be divided into any two parts, the square on the whole line is equal to the sum of the squares on the two parts, together with twice the...
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John Heywood's complete guide to the standard examinations, consisting of 24 ...

Alfonzo Gardiner - 1878
...x, 5a;= ~- + 7. 6. The product of two numbers is 15, and their difference is 2. Find the numbers. 7. If a straight line be divided into any two parts the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and...
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Euclid, books i. & ii., with notes, examples, and explanations, by a late ...

Euclides - 1879
...interpret this formula in terms corresponding to the enunciation of the proposition.] PROPOSITION III. THEOREM. If a straight line be divided into any two parts, the. rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two...
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First Public Examination in Literis Graecis Et Latinis

University of Oxford - 1879
...equal sides be produced the angles on the other side of the base shall be equal to one another. 3. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and...
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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...equal to the rectangle contained by the two parts together with the square on the aforesaid part. 2. If a straight line be divided into any two parts, the squares on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and...
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Moffatt's pupil teachers' course (ed. by T. Page). Candidates, 2nd (-4th) year

Moffatt and Paige - 1879
...rectangle AC, CB together with the square on B C. Therefore, if a straight line, etc. QED Proposition IV. Theorem. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 sider
...but also, and AE-AD+CE; AE = AB.BE=AB.BC; AD-AC.CD = AC.CB, CE= CB\ AB.BC-AC.CB+CB\ Proposition 4. 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 for the Use of Schools and Colleges: With Notes, an ...

Isaac Todhunter - 1880 - 400 sider
...rectangle AC, CB, together with the square on BC. Wherefore, if a straight line &c. QED PKOPOSITION 4. THEOREM. If a straight line be divided into any two parts, the square on the whole line is equal to the squares on the two parts, together with twice the rectangle...
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