| Euclid, Dionysius Lardner - Euclid's Elements - 1828 - 324 pages
...rectangle under either of them and a third of the other, #c. #c. PROPOSITION II. THEOREM. (223) If a right **line (AB) be divided into any two parts (in C), the square of** the whole line is equal to the sum of the rectangles under the whole (AB) and each of the parts (AC,... | |
| John Playfair - Geometry - 1829 - 186 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
...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. Find the... | |
| John Playfair - Euclid's Elements - 1835 - 316 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...be divided into any two parts in C ; the square of** AB is equal to the squares of AC, CB, and to twice the rectangle contained by AC, CB, that is, AB2=... | |
| Euclid - 1835 - 513 pages
...rectangles contained by the whole and each of the parts, are together equal to the square of the whole line. **Let the straight line AB be divided into any two parts in** the point C; the rectangle contained by AB, BC, together with the rectangle * AB, AC, shall be equal... | |
| John Playfair - Geometry - 1836 - 114 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,...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 of AC, CB, and to twice... | |
| Mathematics - 1836 - 472 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 a square... | |
| George Darley - Euclid's Elements - 1836 - 128 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 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... | |
| 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... | |
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