| Euclides - 1855
...produced. Let the straight line AB he bisected at C, and produced to the point D. The rectangle AD.DB, **together with the square of CB, is equal to the square of** C D. Upon CD describe the square CF (I. 46). Join DE. Through B draw BHG parallel to CE or DF (L 31);... | |
| Robert Potts - 1855
...from D, the middle point of BC, DE is drawn perpendicular to AS: shew that BE is, one-fourth of AB. 5. **If a straight line be divided into any two parts, the squares** on the whole line and one of the parts, shall be together equal to twice the rectangle contained by... | |
| Euclides - 1856
...line made up of the half and the part produced. Let AB (Fig. 41) be bisected in C, and produced to D. **The rectangle AD, DB, together with the square of CB, is equal to the square of** C D. Because the line AD is divided into parts at the points C, B, the rectangle AD, BD is equal to... | |
| Euclides - 1860
...unequal segments is equal to the difference between the squares on half the line and the mean distance. **If a straight line be divided into any two parts, the squares** on the whole line, and on one of the parts, are equal to twice the rectangle contained by the whole... | |
| Royal college of surgeons of England - 1860
...angles. 5. Parallelograms upon equal bases and between the same parallels are equal to one another. 6. **If a straight line be divided into any two parts, the squares** on the whole line and one of the parts are equal to twice the rectangle contained by the whole and... | |
| Robert Potts - 1860 - 361 sider
...CB, together with the square on BC. If therefore a straight line be divided, &c. QED PROPOSITION IV. **THEOREM. 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... | |
| War office - 1861 - 12 sider
...to it. 2. Triangles upon the same base, and between the same parallels, are equal to one another. 3. **If a straight line be divided into any two parts, the squares** on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and... | |
| Woolwich roy. military acad - 1861
...expect to find the " differences " largest at the early part of the table and gradually decreasing. 14. **If a straight line be divided into any two parts, the squares** on the whole line and on one of the parts are equal to twice the rectangle contained by the whole and... | |
| Euclides - 1862
...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** tin gnomon CMG, and the figure LG; but the gnomon CMG and LG make up the whole figure CEFD, which is... | |
| Euclides - 1862
...and by A and EC. Conclusion. — Therefore, if there be two straight lines, &c. QED PROPOSITION 2.— **THEOREM. If a straight line be divided into any two parts, the** rectangles contained by the whole line and each of its parts, are together equal to the square on the... | |
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