| John Playfair - 1855 - 317 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 - 400 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
...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 - 410 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
...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
...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 - 285 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 - 349 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
...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... | |
| Henry Major - 1873
...AC, together with the rectangle AB, BC, is equal to the square of AB. III. — If a straight line lie **divided into any two parts, the rectangle contained...contained by the two parts, together with the square** of the aforesaid part. Let AB be divided into any two parts in the point C; then the rectangle AB,... | |
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