 | Euclides - 1853 - 146 σελίδες
...BC. If, therefore, a straight line, &c. QED PROP. IV. THEOREM. 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. 3 Let the straight line AB be divided into any two parts in C; the... | |
 | Royal Military Academy, Woolwich - 1853 - 400 σελίδες
...therefore a straight line, etc. QE n. PROPOSITION IV. THEOR. 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... | |
 | William Frederick Greenfield - 1853 - 228 σελίδες
...a number is obtained by multiplying the square by the number. Now the square is equal to the sum of the squares of the two parts together with twice the product of the parts. If this be now multiplied by oue of the parts, the result will be the cube of the first part, twice... | |
 | Euclides - 1853 - 176 σελίδες
...called the rectangle ab, ac. Я PROPOSITION IV. — THEOREM. If a straight line be divided into any two parts, the square of the whole line is equal to the squares oftíie two parts, togetlwr with twice the rectangle contained by the parts. LET the straight line... | |
 | Euclides - 1853 - 334 σελίδες
...THEOE. If a straight line be divided into any two parts: then the square of the whole line shall be equal to the squares of the two parts together with twice the rectangle contained by the two parts. Let the straight line AB be divided into any two parts AC, CB... | |
 | Allan Menzies - 1854 - 520 σελίδες
...out the part of your demonstration in which it is evaded. 3. 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 modification of what you have here proved constitutes the rule... | |
 | Upper Canada. Chief Superintendent of Schools - 1854 - 196 σελίδες
...7th, 27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. 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 their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts ;... | |
 | William Somerville Orr - 1854 - 534 σελίδες
...THEOREM. If a straight line (AB) be divided into any two parts (А С, С В) the square of the wlak line is equal to the squares of the two parts, together with twice the rectangle contained by the parts : that is, А В1 = А С* + С Вг + twice А ОС В. * 46 I. Upon... | |
 | Thomas Lund - 1854 - 520 σελίδες
...opposite, .-. / ACS = / BCD = a right angle. 44. PROP. XXII. If a straight line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the two parts together with twice the rectangle* contained by the parts. QDEF.... | |
 | 1855 - 424 σελίδες
...often be rendered much more simple and concise than in ordinary language. The proposition, (Euclid 4, 2,) that when a straight line is divided into two...twice the product of the parts, is demonstrated, by squaring a binomial. Let the side of a square be represented by » ; And let it be divided into two... | |
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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. 
