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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 ... - Página 43
por Euclides - 1814
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The Pupil teacher, a monthly educational journal. H. Major, ed

Henry Major
...equal, and one side and an adjacent, angle equal, each to each, they shall be equal in all respects. 2. 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 College calendar. [Continued as] The College calendar for the United ...

Scotland free church
...equal to one another. Or—Any two angles of a triangle are together less than two right angles. 3. 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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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 443 páginas
...middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM. If a straight line is divided into any two parts, the square of the whole line is equivalent to the squares of the two parts, together with twice the rectangle contained by the parts....
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Elements of Plane Geometry, Parte1

Thomas Hunter - 1878 - 132 páginas
...because AB=BD. Therefore AB"=AB. AC+AB.CB. PROPOSITION XVI.—THEOREM. If a straight line be divided into two parts, the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle contained by the parts. Let AB be a straight...
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Complete guide to the certificate and scholarship examinations, by a head ...

J T. Amner - 1878
...that four right-angled triangles of equal area can be drawn having the same hypotenuse. Section 3. 1. 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 Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 266 páginas
...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,...together with twice the rectangle contained by the two part*. Let the straight line AB be divided into any two parts in C; then will . CB. Upon AB describe...
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Geometry, Old and New, Its Problems and Principles: A Paper

Benjamin Gratz Brown - 1879 - 48 páginas
...arise from this source which maybe developed either numerically or geometrically ; such as that, if a line be divided into any two parts the square of the...together with twice the rectangle contained by the parts. This proposition is one of first consequence, as having furnished the key to the extraction of the...
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A complete set of male pupil teachers' examination questions in Euclid [book ...

W J. Dickinson - 1879 - 36 páginas
...one part may be twice the square on the other part. 4. Define a rectangle and a square. Prove that if a straight line be divided into any two parts, the square on the whole line is equal to the squares of the two parts, together with twice the rectangle contained...
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Moffatt's scholarship answers, by T.J. Livesey (T. Page).

Moffatt and Paige - 1879
...square be described upon the semi-diameter of another square; compare the areas of the squares. 3. 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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Mathews' Euclid examination papers ... on Euc. i.-iv

Edward Harri Mathews - 1879
...EFGH is inscribed, show that the sides of ABCU are equally divided by the points E, F, G and H. 3. 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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