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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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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...the same base and on the same side of it, are between the same parallels. Section 5. 1. If a right line be divided into any two parts, the squares of the whole line and one of the parts are equal to twice the rectangle contained by the whole line and that part, together...
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Report of the Committee of Council on Education (England and Wales ..., Utgave 2

Great Britain. Council on Education - 1848
...the same base, and on the same side of it, are between the same parallels. Section 5. 1. If a right line be divided into any two parts, the squares of the whole line and one of the parts are equal to twice the rectangle contained by the whole line and that part, together...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...the rectangle contained by the two parts, together with the square of the aforesaid part. PROP. IV. 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 first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 sider
...equal to the rectangle AD, DB : Add to each of these LG, which is equal to the square of CB, therefore the rectangle AD, DB, together with the square of CB, is equal to the gnomon CMG and the figure LG : But the gnomon CMG and LG make up the whole figure CEFD, which is the...
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Minutes of the Committee of Council on Education, Volum 1

Great Britain. Committee on Education - 1850
...the squares of the two parts, together with twice the rectangle contained hy the parts. 2. Show that if a straight line be divided into any two parts, the squares of the whole line and one of the parts are equal to twice the rectangle contained by the whole and that part together with...
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Papers for the schoolmaster, Volumer 1-6

...Student*. 1. Parallelograms upon the same base and between the same parallels are equal to one another, 2. If a straight line be divided into any two parts, the squares of the whol« line, and of one of the parts, are equal to twice the rectangle contained by the whole and that...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...half and the part produced. Let the straight line AB be bisected in C, and produced to the point D; the rectangle AD, DB, together with the square of CB, is equal to the square of CD. • xlvi. i. Upon CD describe* the square CEFD, join DE, " xxxi i. and through B draw b BHG parallel...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - 1853
...equal (4. Cor. n.) to DB : therefore the gnomon CMG is equal to the rectangle AD, DB : c F therefore the rectangle AD, DB, together with the 'square of CB, is equal to the gnomon CMG, and the figure LG ; But the gnomon CMG and LG make up the whole figure CEFD, which is the...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 sider
...two 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 oftíie two parts, togetlwr with twice the rectangle...
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Elements of geometry and mensuration

Thomas Lund - 1854 - 192 sider
...very elegant proof of the important Theorem in (43) may be given as follows :— 45. PROP. XXIII. Jf a straight line be divided into any two parts, the squares of the whole line and one of the parts are together equal to twice the rectangle contained by the whole and that part, together...
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