| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| ...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... | |
| 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... | |
| 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... | |
| 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... | |
| 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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