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" 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 contained by the parts. "
The Elements of Euclid; viz. the first six books, together with the eleventh ... - Page 45
by Euclides - 1814
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...Parallelograms on the same base and between the same parallels, are .equal to each other. 7. If a right line be divided into any two parts, the square of...together with twice the rectangle contained by the parts. 8. Describe a square that shall be equal to a given rectilineal figure. 9. Find the centre of a given...
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National Society's Monthly Paper

1856
...angles ; and the three interior angles of every triangle are together equal to two right angles. 5. If a straight line be divided into any two parts,...of the two parts, together with twice the rectangle contamed by the parts. 6. In obtuse-angled triangles if a perpendicular be drawn from either of the...
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Manual of Method for the use of teachers in elementary schools

W. F. RICHARDS - Education, Primary - 1856 - 184 pages
...a given triangle, and have one of its angles equal to a given rectilineal angle. Section II. — 1. If a straight line be divided into any two parts, the square of the whole line shall be equal to the sum of the squares of the parts, together with twice the rectangle contained...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...Cor. 1. — By making A equal to the whole line considered as divided into two parts, it appears that if a straight line be divided into any two parts, the square of the whole liriiHs equal to the sum of the rectangles contained by the whole line and each of the parts. Cor....
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Parliamentary Papers, Volume 25

Great Britain. Parliament. House of Commons - Bills, Legislative - 1858
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. 6. PROP. IX. — If a straight line be divided into two equal, and also into two unequal parts ; the...
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Report of Her Majesty's Civil Service Commissioners: Together with ..., Volume 3

1858
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. 6. PROP. IX. — If a straight line be divided into two equal, and also into two unequal parts ; the...
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Elements of Geometry and Conic Sections

Elias Loomis - Conic sections - 1858 - 234 pages
...THEOREM. If a straight line is divided into any two parts, the square oj the whole line is equivalent to the squares of the two parts, together with twice...AB be divided into any two parts in C ; the square on AB is equivalent to the squares on AC CB, together with twice the rectangle contained by AC, CB...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873
...rectangle AB, BC, is equal to the rectangle AC, CB, together with the square of BC. -If a straiyht line be divided into any two parts, the square of...together with twice the rectangle contained by the "tarts. ca Let AB be divided into any two parts in C ; then the square of AB shall be equal to the...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...rectangle AB, AC is equal to the rectangle AC, CB together with the square on AC. PROPOSITION 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 contained...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874
...with the square on BC. If therefore a straight line be divided, &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 squares on the two parts, together with twice the rectangle contained...
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