 | Euclid - 1835 - 540 σελίδες
..." If, therefore, a straight line," &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the square of the whole line is equal to...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... | |
 | John Playfair - 1836 - 148 σελίδες
...equal so one another. Which was te be proved. PROP. XX. THEOR. If a straight line be divided into any two parts, the square of the whole line is equal to...squares of the two parts, together with twice the rectangle contained by the parts. Let the straight line AB he divided into any two parts in C ; the... | |
 | 1836 - 488 σελίδες
...two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts, the square of the whole line is equal to...squares of the two parts, together with twice the rectangle contained by the parts. Сок. From the demonstration, it is manifest that the parallelograms... | |
 | George Darley - 1836 - 172 σελίδες
...CB, that is, the rectangle under AC and CB. This, &c. ART. 92. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts together with twice the rectangle under the parts. Let AB he a right... | |
 | Charles Reiner - 1837 - 246 σελίδες
...M.- — Express this truth as a general proposition. P. — If a straight line be divided into any two parts, the square of the whole line is equal to...squares of the two parts, together with twice the rectangle contained by the parts. The master will, here, have a suitable opportunity of directing the... | |
 | Euclides - 1837 - 112 σελίδες
...and that these are = AC x CB + CB*. PROPOSITION IV. Theorem. 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. * By the rectangle AX BC (the lines A and BC being separate) is'... | |
 | Andrew Bell - 1837 - 290 σελίδες
...CB, together with the square of BC. PROPOSITION TV. THEOREM. If a straight line be divided into any two parts, the square of the whole line is equal to...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... | |
 | Euclid, James Thomson - 1837 - 410 σελίδες
...with the rectangle AC.CB. * If, therefore, &c. PROP. IV. THEOR. 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 their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is... | |
 | Bewick Bridge - 1839 - 280 σελίδες
...infer, that " if a number be divided into two parts, the square of the number is equal to the sum of the squares of the two parts, together with twice the product of those parts." 31. Let a and b be any two numbers ; then Their difference^*! — 6 The difference of... | |
 | Dionysius Lardner - 1840 - 386 σελίδες
...several rectangles under the line and each of its parts. (242.) If a line be divided into two or more parts, the square of the whole line is equal to the squares of the several parts together with twice the rectangles under every pair of parts. Let theline AB (fig.l 1... | |
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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. 
