| 1851
...by those two sides is a right angle, . . 3. If a straight line be divided into any two parts, _ 20 2 **the square of the whole line is equal to the squares of the two parts, together with twice** their rectangle, 4. In any plane triangle the sides are to each 21 other as what ? Demonstrate this... | |
| Euclides - 1852 - 152 pages
...(squared or) multiplied by 7 is equal to 49. These added together make up 84.] BOOK n. PEOP. IV. THEOE. 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... | |
| Education - 1863 - 818 pages
...between the first and second shall be equal to that intercepted between the second and third. 5. If **a straight line be divided into any two parts, the square of the whole line is equal to the squares** on the two parts, together with twice the rectangle contained by the parts. Entrance Examination. 6.... | |
| Euclides - 1853 - 146 pages
...AC, CB, together with the square of BC. If, therefore, a straight line, &c. QED PROP. IV. THEOREM. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** 3 Let the straight line AB be divided into any two parts in C; the square of AB is equal to the squares... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...together with the square of BC. If therefore a straight line, etc. QE n. PROPOSITION 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... | |
| Euclides - Geometry - 1853 - 176 pages
...lines ab, ас is sometimes simply 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 - Geometry - 1853 - 334 pages
...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 in c. Then the square of AB... | |
| Allan Menzies - 1854 - 520 pages
...Euclid's general reasoning, and point out the part of your demonstration in which it is evaded. 3. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** A modification of what you have here proved constitutes the rule for the extraction of the square root.... | |
| Upper Canada. Chief Superintendent of Schools - Education - 1854 - 196 pages
...required in the demonstrations of the 7th, 27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. If **a straight line be divided into any two parts, the...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 - Science - 1854 - 532 pages
...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 А В describe the square AE... | |
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