 | 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 - 384 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 - 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... | |
 | Euclides - Euclid's Elements - 1837 - 112 pages
...showing that AB x BC = figures AD + CE, and that these are = AC x CB + CB*. PROPOSITION IV. Theorem. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. * By the rectangle AX BC (the lines A and BC being separate) is' meant the rectangle which may be formed... | |
 | Charles Reiner - Geometry - 1837 - 254 pages
...twice the rectangle contained by ac and c b. M.—Express this truth as a general proposition. P.—If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. The master will, here, have a suitable opportunity of directing the attention of his pupils to a numerical... | |
 | Euclid, James Thomson - Geometry - 1837 - 410 pages
...equal to the square of BC, together with the rectangle AC.CB. * If, therefore, &c. PROP. IV. THEOR. IF a straight line be divided into any two parts, the...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... | |
 | Andrew Bell - Euclid's Elements - 1837 - 290 pages
...twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BO, are equal to twice the rectangle AB-BC, together with the square... | |
 | Robert Simson - Geometry - 1838 - 434 pages
...rectangle 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...the rectangle contained by AC, CB. Upon AB describe (46. 1.) the square ADEB, and join BD, and through C draw (31. 1.) CGF parallel to AD or BE and through... | |
 | Euclides - 1838 - 264 pages
...equal to the rectangle contained by the two parts, together with the square of the aforesaid part. Let the straight line AB be divided into any two parts in the point C : the rectangle AB-BC shall be equal to the rectangle AC-CB, together with the square of... | |
 | Jeremiah Day - Algebra - 1839 - 354 pages
...than in ordinary language. The proposition, (Enc. 4. 2.) thai when a straight line is divided into two parts, the square of the whole line is equal to the squares of the iwo parts, together with twice the product of the parts, is demonstrated, by involving a binomial.... | |
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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. 
