CB ; wherefore the four figures HF, CK, AG, GE are equal to the squares of AC, CB, and to twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square of AB: therefore the square of AB is equal to the squares of AC,... Elements of geometry: consisting of the first four,and the sixth, books of ... - Page 47by Euclides - 1842Full view - About this book
| Euclides - 1864 - 262 pages
...whole figure ADEB, which is the square on AB ; therefore the square on AB is equal to the squares on AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line be divided, &c. QED COR. From the demonstration, it is manifest, that the parallelograms about the... | |
| Euclides - 1864 - 448 pages
...whole figure ADEB, which is the square on AB ; therefore the square on AB is equal to the squares on AC, CB, and twice the rectangle AC, CB. Wherefore, if a straight line be divided, &c. QED COR. From the demonstration, it is manifest, that the parallelograms about the... | |
| Euclides - 1865 - 402 pages
...because the angle at D is a right angle, the angle ACB is greater than a right angle ; (i. 16) and therefore the square of AB is equal to the squares of AC, CB, and twice tiie rectangle BC, CD; (n. 12) to each of these equals add the square of BC, then the squares of AB,... | |
| Robert Potts - 1865 - 528 pages
...figures HF, CK, AG, GE, are equal to the squares on AC, CB, and twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the square on AB ; therefore the square on AB is equal to the squares on AC, CB, and twice the rectangle AC, CB.... | |
| Gerardus Beekman Docharty - Geometry - 1867 - 474 pages
...up of the four figures, viz., the two squares AF, FD, and the two equal rectangles EF, FB. That is, the square of AB is equal to the squares of AC, CB, together with twice the rectangle of AC, CB. QED Corol. Hence, if a line be divided into two equal... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 426 pages
...which is the square on AB. Therefore the square on AB is equal to the squares on AC, CB, together with twice the rectangle AC, CB. "Wherefore, if a straight line &c. QED COROLLARY. From the demonstration it is manifest, that parallellograms about the diameter of a square... | |
| Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 424 pages
...which is the square on AB. Therefore the square on AB is equal to the squares on AC, CB, together with twice the rectangle AC, CB. Wherefore, if a straight line &c. QED COROLLARY. From the demonstration it is manifest, that parallellograms about the diameter of a square... | |
| Robert Potts - 1868 - 434 pages
...whole figure ADEB, which is the square on AB ; therefore the square on AB is equal to the squares on AC, CB, and twice the rectangle AC, CB. "Wherefore, if a straight line be divided, &c QED COB. From the demonstration, it is manifest, that the parallelograms about the diameter... | |
| Henry William Watson - Geometry - 1871 - 320 pages
...AC and CH, ie of AC and CB. Similarly, HE is the rectangle of HG and GE, ie of CB Fig. 29. and AC, therefore the square of AB is equal to the squares of AC and CB, together with twice the rectangle of AC and CB. Again, make the same construction as in the... | |
| Henry Major - Student teachers - 1873 - 580 pages
...figures HF, CK, AG, GE, are equal to the squares of AC, CB, and twice the rectangle AC, CB : but HF, CK, AG, GE make up the whole figure ADEB, which is the...of AB is equal to the squares of AC, CB, and twice t'ue rectangle AC, CB. Coa. The parallelograms about the diameter of it square, are likewise squares.... | |
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