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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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Papers for the schoolmaster, Volume 3

1867
...undivided line, and tho several parts of the divided line. 2. If a straight line be divided into any to parts, the square of the whole line is equal to the...together with twice the rectangle contained by the parts. Prove geometrically that the sum of the squares of two lines cannot be less than twice their rectangle....
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University of Durham

University of Durham - Education, Higher - 1851
...Equal triangles upon the same base and upon the same side of it are between the same parallels. 4. If a straight line be divided into any two parts, the square of the whole line is equal to the square of the parts together with twice the rectangle contained by the parts. 5. To divide a given...
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Annual Report of the Commissioners ...

1851
...by those two sides is a right angle, . . 3. If a straight line be divided into any two parts, _ 20 2 the square of the whole line is equal to the squares of the two parts, together with twice their rectangle, 4. In any plane triangle the sides are to each 21 other as what ? Demonstrate this...
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General Report on Public Instruction in the Bengal Presidency

Education - 1863
...intercepted between the first and second shall be equal to that intercepted between the second and third. 5. If a straight line be divided into any two parts,...the square of the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts. Entrance Examination. 6....
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...rectangles contained by the whole and each of the parts are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C; the rectangle contained by AB, BC ; together with the rectangle* AB, AC, shall be equal...
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...AC, CB, together with the square of BC. If, therefore, a straight line, &c. QED PROP. IV. THEOREM. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. 3 Let the straight line AB be divided into any two parts in C; the square of AB is equal to the squares...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 147 pages
...straight lines ab, ас is sometimes simply called the rectangle ab, ac. Я PROPOSITION IV. — THEOREM. If a straight line be divided into any two parts,...the square of the whole line is equal to the squares oftie two parts, togetlwr with twice the rectangle contained by the parts. LET the straight line...
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The Elements of Euclid. Books I.-VI.; XI. 1-21 XII. 1-2. A New Text ..., Book 1

Euclides - Geometry - 1853
...THEOE. If a straight line be divided into any two parts: then the square of the whole line shall be equal to the squares of the two parts together with twice the rectangle contained by the two parts. Let the straight line AB be divided into any two parts AC, CB in c. Then the square of AB...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

Euclid - Geometry - 1853 - 136 pages
...then (a) I. 46. (6 VI. 31. (c) Constr. (/) I. 34. a'2 = am -f- a n. PROPOSITION III. THEOREM. — If a straight line (AB) be divided into any two parts (in C), the rectangle under the whole line (AB) and one of those parts (CB) is equal in area to the square on that...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853
...rectangles contained by the whole and each of the parts are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C ; the rectangle contained by AB, BC, together with the rectangle* AB, AC, shall be equal...
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