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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 ... - Seite 41
von Euclides - 1816 - 528 Seiten
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Elementary Geometry: With Applications in Mensuration

Charles Davies - 1850 - 218 Seiten
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. Let the line AB be divided into two -^ HC parts at the point E : then will the square described on AB be equivalent...
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Elementary Geometry: With Applications in Mensuration

Charles Davies - 1850 - 236 Seiten
...parts, the square described on the whole line is equivalent to the sum of the squares described on the two parts, together with twice the rectangle contained by the parts. . Let the line AB be divided into two n IT n parts at the point E: then will the square described on AB be equivalent...
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Papers for the schoolmaster, Bände 1-6

582 Seiten
...contained by the whole and one of the parts, shall be equal to the square of the other part. 2. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. In what sense is the area of a triangle said to be equal to half the product of tils base and altitude?...
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Papers for the Schoolmaster, Band 2

1852 - 314 Seiten
...a given triangle, and have one of its angles equal to * Riven rectilineal angle. SECTION II. 1. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the paits. 2. If a straight line be divided into two equal and also into two unequal parts, the squares...
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Papers for the schoolmaster, Band 3

1867 - 336 Seiten
...undivided line, and tho several parts of the divided line. 2. If a straight line be divided into any t»o 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 - 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

1863 - 818 Seiten
...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 - 152 Seiten
...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 - 146 Seiten
...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, the...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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