 | Euclides - 1865 - 402 páginas
...equal to the rectangles under the whole and each of the parts . . . . . II. 2. 2. The rectangle under the whole and one of the parts, is equal to the rectangle under the two parts, together with the square on the aforesaid part . . . . . . . n. 3. 3. The square... | |
 | John Playfair - 1855 - 350 páginas
...multiplying both members of this equality by a, we shall have a2=«A + a</ PE Q KLD PROP. III. THEOR. tf a straight line be divided into any two parts, the...the parts, is equal to the rectangle contained by the tttm parts, together with the square of the aforesaid part. Let the straight line AB be divided... | |
 | Euclid, Isaac Todhunter - 1867 - 424 páginas
...AB, BC, is equal to the square on AB. Wherefore, if a straight line &c. QED PROPOSITION 3. THEOREM. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. Let the straight line AB be divided into any two parts at the point (7: the rectangle AB, BC shall... | |
 | 1867 - 224 páginas
...one another, and likewise those which are terminated at the other extremity equal to one another. 3. If a straight line be divided into any two parts,...parts, together with the square on the aforesaid part. 4. Make a triangle of which the sides shall be equal to three given straight lines, but any two whatever... | |
 | Robert Potts - 1868 - 434 páginas
...DA is equal to AB : and CE is contained by AB, BC, for BE is equal to AK : PROPOSITION III. THEOREM. If a straight line be divided into any two parts, the rectangle contained ky the whole and one of the parts, is equal to the rectangle contained by the twa parts, together with... | |
 | Euclides - 1871 - 136 páginas
...CB. QED • Ex. The square on a straight line is equal to four times tlie square on half the line. If a straight line be divided into any two parts,...parts together with the square on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB, CB = sum of rect. AC, CB... | |
 | Edinburgh univ - 1871 - 392 páginas
...triangles, what things must be equal, in order that the triangles may be equal in every respect ? 3. If a straight line be divided into any two parts,...contained by the two parts, together with the square of the foresaid part. 4. Equal straight lines in a circle are equally distant from the centre; and... | |
 | Henry William Watson - 1871 - 320 páginas
...of the parts AE and EB, and the rectangle of CD and EB would be equal to the square of EB, therefore If a straight line be divided into any two parts, the rectangle of the whole line and one of the parts will be equal to the rectangle of the two parts, together with... | |
 | Euclides, James Hamblin Smith - 1872 - 376 páginas
...square on a straight line is equal to forr times the square on half the line. PROPOSITION III. THEOREM. If a straight line be divided into any two parts,...parts together with the square on the aforesaid part. Let the st. line AB be divided into any two parts in C. Then must rect. AB, CB = sum of rect. AC, CB... | |
 | Euclid, Charles Peter Mason - 1872 - 216 páginas
...the same as the rectangles under the whole line BC and each of its parts. PBOPOSITION III. If a right line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangle contained... | |
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If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part. 
