 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
 | Euclid, James Thomson - Geometry - 1845 - 382 pages
...the squares of ACT CB, and twice the rectangle AC.CB. But HF, CK, AG, 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 AC.CB.* Wherefore, &c. Cor. 1. It follows from this demonstration,... | |
 | Euclides - 1845 - 546 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 the rectangle BC, CD ; (n. 12.) to each of these equals add the square of BC ; therefore the squares of AB, BC are... | |
 | Euclid - Geometry - 1845 - 218 pages
...the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB. Upon AB describe* the square ADEB, and join BD, * 46. i.... | |
 | Euclides - 1846 - 292 pages
...CK, AG, GE are together 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...therefore the square of AB is equal to the squares of AC,CB, and twice the rectangle AC, CB. Wherefore, If a straight line, Sfc. <j. ED COR. From the demonstration,... | |
 | Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C ; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB2=AC2+CB2+2AC.CB. Upon AB describe (Prop. 46.... | |
 | Euclides - 1846 - 272 pages
...opposite side the pependicular AF, and as one of the angles ACB and ACP is obtuse, let ACB be obtuse, and therefore the square of AB is equal to the squares of AC and of CB, together with twice the rectangle underBC and CF, (by Prop. 12. B. 2), but the angle ACP... | |
 | Euclides - 1848 - 52 pages
...is equal to the squares of the two parts, together with twice the rectangle contained by the parts. COR. From the demonstration, it is manifest, that...diameter of a square are likewise squares. PROP. V. THEOREM. If a straight line be divided into two equal parts, and also into two unequal parts ; the... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...aides of a square; wherefore the angle Let the straight line AB be divided into any two parts in c; the square of AB is equal to the squares of AC, CB, together with twice the rectangle contained by AC, CB. CGB is equal to the angle GBC; and therefore... | |
 | Euclides - 1852 - 152 pages
...the rectangle contained by the parts, Let the straight line AB be divided into any two parts in C; the square of AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB. • xlvi. i. Upon AB describe* the square ADEB, and join... | |
 | Euclides - Geometry - 1853 - 334 pages
...HG, CK, AF, FE are equal to the squares of AC, CB and twice the rectangle AC, CB ; and HG, CK, AF, FE make up the whole figure ADEB, which is the square...the square of AB is equal to the squares of AC, CB together with twice the rectangle AC, CB. Which was to be proved. COR. — If through any point in... | |
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