 | Euclides - 1846 - 292 pages
...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 contained by the parts. Let the straight line AB be divided into any two parts in C : the square of AB shall be equal to the squares... | |
 | Euclides - 1848 - 52 pages
...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 contained by the parts. COR. From the demonstration, it is manifest, that the parallelograms about the diameter of a square... | |
 | Elias Loomis - Conic sections - 1849 - 252 pages
...straight line is divided into any two parts, the square of the whole line is equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts. Let the straight line AB be divided into any two parts in C; the square on AB is equivalent to the squares... | |
 | Euclid, Thomas Tate - 1849 - 120 pages
...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 contained by the parts. Upon AB describe (i. 46.) the square ADEB, and join BD, and through c draw (i. 31.) CGF parallel to... | |
 | Charles Davies - Geometry - 1850 - 238 pages
...is equivalent to the product of ADxAE; that is, to CGx(AB+DC) ; and consequently, the trapezoid ABCD is equal to half that product. THEOREM XI. If a line...the parts. . Let the line AB be divided into two n IT n parts at the point E: then will the square described on AB be equivalent to the two squares described... | |
 | 1867 - 336 pages
...straight line be divided into any t»o parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Prove geometrically that the sum of the squares of two lines cannot be less than twice their rectangle.... | |
 | Charles Davies - Geometry - 1886 - 340 pages
...is, to CG x (AB+DC) ; and consequently the trapezoid ABCD is equal to half that productTHEOREM XIIf a line be divided into two parts, the square described...on the two parts, together with twice the rectangle container! by the parts Let the line AB be divrled into two n tr /-* ,L/_ fl parts at the point E:... | |
 | Euclides - 1852 - 152 pages
...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 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,... | |
 | Education - 1863 - 830 pages
...a straight line be divided into any two parts, the square of the whole line is equal to the squares on the two parts, together with twice the rectangle contained by the parts. Entrance Examination. 6. Describe a square that shall be equal to a given triangle. 7. (a) Equal chords... | |
 | Adrien Marie Legendre - Geometry - 1852 - 436 pages
...A0*o= BDx BC+DCxBC=c^= (BD+DC}x BCoBCxBCoBG1•, that is, the square described on the hypothenuse BC is equivalent to the sum of the squares described on the two sides BA, A 0. Thus, we again arrive at this property of the right-angled triangle, and by a path very... | |
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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 contained by the parts. 
