| Robert Simson - Trigonometry - 1827 - 513 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, 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 shall be equal to the... | |
| Jeremiah Day - Algebra - 1827 - 332 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 - 186 pages
...equal to the rectangle contained by the two parts together with the square of the foresaid part. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the** two parts. Or, in other words, the square of the sum of two lines is greater than the sum of their... | |
| Education - 1833
...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, the...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. Find the... | |
| 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, 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 squares... | |
| John Playfair - Geometry - 1836 - 114 pages
...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, the...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 squares... | |
| Mathematics - 1836 - 472 pages
...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, the...together with twice the rectangle contained by the parts.** Сок. From the demonstration, it is manifest that the parallelograms about the diameter of a square... | |
| 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 - 344 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... | |
| William Grier - Mechanical engineering - 1836 - 380 pages
..., and AD 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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