 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 - 1874 - 342 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 16. The square on AB is equal to the squares on AC, CB, and twice the rectangle AC,... | |
 | Edward Atkins - 1874 - 426 pages
...CB. ifj^CB Therefore, if a straight line, &c. QED COROLLARY. — From this demonstration it follows that the parallelograms about the diameter of a square are likewise squares. Proposition 5. — Theorem. If a straight line be divided into two equal parts, and also into two unequal... | |
 | Robert Potts - Geometry - 1876 - 446 pages
...squares on AC, CB,and twice the rectangle AC, CB. Wherefore, if a straight line be divided, &c Q..ED COE. From the demonstration, it is manifest, that the parallelograms...about the diameter of a square, are likewise squares • -i •• PROPOSITION V. THEOREM. :.,.t If a straight line be divided into two equal parts, and... | |
 | Edward Atkins - 1876 - 130 pages
...AG, GE are equal to the squares on AC and CB, together with twice the rectangle AC, CB. But HF, CK, AG, GE, make up the whole figure ADEB, which is the square on AB ; j-'\^hole Therefore the square on AB is equal to the squares on A~B'/lor AC and CB and twice... | |
 | Moffatt and Paige - 1879 - 506 pages
...CK, AG, GE are together 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 A B. Therefore the square on AB is equal to the squares on AC, CB and twice the rectangle AC, C... | |
 | Isaac Todhunter - Euclid's Elements - 1880 - 426 pages
...CK, AG, GE&ro equal to the squares on AC, CB, together with 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, together with twice the rectangle... | |
 | Euclides - Euclid's Elements - 1881 - 236 pages
...CB, with twice the rectangle AC.CB. But the figures HF, CK, AG and GE make up the whole figure AE, which is the square of AB. Therefore the square of AB is equal to the squares of AC and CB, and twice the rectangle 4 C. CB. Wherefore, if a straight line be divided, &c. QED Con. 1.... | |
 | Euclid, Isaac Todhunter - Euclid's Elements - 1883 - 428 pages
...CK, AG, GEsate equal to the squares on AC, CB, together with 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, together with twice the rectangle... | |
 | Civil service commission - 1883 - 62 pages
...Saturday, ЗШ June, 1883, 2 PM to 5 PM (Great importance will be attached to accuracy.) 1, — Prove that the parallelograms about the diameter of a square are likewise squares. Sol. This is proved in Eue. II. 4, and is stated as a corollary to that proposition. g. — (1) Divide... | |
 | Stewart W. and co - 1884 - 272 pages
...the triangle ABC. Then, because D is a right angle, the angle ACB is greater than aright angle; and the square of AB is equal to the squares of AC, CB, and twice the, rectangle uci, BC, CD ; to each add the square of BC ; therefore the squares of AB, BC are equal to the square... | |
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