 | Bewick Bridge - 1821 - 284 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." . 1 E 31. Let 31. Let a and b be any two numbers; then, The difference of their Сubes=a3—b3... | |
 | 1854 - 1112 σελίδες
...parallel to both these cases ; for, as Euclid tells us (II., 4), 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 ; and, were we to represent the line as a divided into two parts m,... | |
 | Charles Tayler - 1824 - 350 σελίδες
...iv. Book ii., viz., that If a number be divided into any two parts, the square of the •whole number is equal to the squares of the two parts, together with twice the product (or rectangle) of the twojiarts. For (c) Prime numbers are such as cannot be represented by factors,... | |
 | Peter Nicholson - 1825 - 1046 σελίδες
...', If a straight line be divided into any two parts, the square or in* ELEMENTS OP KUCUD. 191 vhole 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 С ; the... | |
 | Euclid, John Playfair - 1826 - 326 σελίδες
...Therefore, if a straight line, &e. QED C B D E 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 twiee the reetangle eontained by the parts. Let the straight line AB be divided into any two parts... | |
 | Euclid - 1826 - 234 σελίδες
...and it be ag =fg + g2. Q- ED PROPOSITION IV. THEOREM. If a right line be divided into any two part:!, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained under the parts. Let the right line AB be divided into any two parts in the point... | |
 | Jeremiah Day - 1827 - 352 σελίδες
...length, be AB, the breadth BC, and the depth CO, the expression for the solid contents wiH be, ABx.BCXCO. 524. By means of the algebraic notation, a geometrical...by s ; And let it be divided into two parts, a and b. By the supposition. s=a-\-b And squaring both sides, s3=a3+2o6+63. That is, s^ the square of the... | |
 | Robert Simson - 1827 - 546 σελίδες
...of BC. If therefore a straight line, &c. QED PROP. IV. THEOK. 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 - 1829 - 210 σελίδες
...the two parts together with the square of the foresaid part. 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 two parts. Or, in other words, the square of the sum of two lines is greater... | |
 | 1833 - 412 σελίδες
...two parts together with the square of the aforesaid part. 5. 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. a. Find the value of x in x1 — a x-\-b*^0. b. Divide a*— 3x*+x*... | |
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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. 
