 | Robert Simson - Trigonometry - 1827 - 546 pages
...rectangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOK. If a straight line be divided into any 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... | |
 | Jeremiah Day - Algebra - 1827 - 352 pages
...than in ordinary language. The proposition, (Euc. 4- 2.) that when a straight line is divided into two parts, the Square of the whole line is equal to...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented... | |
 | John Playfair - Geometry - 1829 - 210 pages
...-\- b. Multiply this equation by d, then sb = ab + 66, which is the prop. PROPOSITION IV. THEOREM. If a straight line be divided into any two parts, the square cf the whole line is equal to the squares of the two parts together with twice the rectangle contained... | |
 | Education - 1833 - 412 pages
...equal to the rectangle contained by the two parts together with the square of the aforesaid part. 5. If a straight line be divided into any 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* + J x'-l'2x + 6 by ^-3.... | |
 | Euclid - 1835 - 540 pages
...AC, CB together with the square of BC. " If, therefore, a straight line," &c. QED PROP. IV. THEOR. If a straight line be divided into any 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... | |
 | John Playfair - Euclid's Elements - 1835 - 336 pages
...therefore, multiplying both members of this equality by c, we shall have ac = bc-\-c2. PROP. IV. THEOR. Tf a straight line be divided into any two parts, the...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... | |
 | Mathematics - 1836 - 488 pages
...equal to the rectangle contained by the two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. Сок. From the demonstration, it is manifest that the parallelograms about the diameter of... | |
 | John Playfair - Geometry - 1836 - 148 pages
...the diagonal of any parallelogram, are equal so one another. Which was te be proved. PROP. XX. THEOR. If a straight line be divided into any 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 square of AB is equal to the... | |
 | George Darley - Euclid's Elements - 1836 - 172 pages
...the rectangle under DE and 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... | |
 | William Grier - Mechanical engineering - 1836 - 380 pages
...and 9 BC Al) and EF, and AD and FB: thus expressed, AD. AB = AD . AE+ AD . EF + AD . FB.* If a right line be divided into any two parts, the square of the whole line, is equal to both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any... | |
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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. 
