| 1867
...undivided line, and tho several parts of the divided line. 2. If a straight line be divided into any t»o **parts, the square of the whole line is equal to the...together with twice the rectangle contained by the parts.** Prove geometrically that the sum of the squares of two lines cannot be less than twice their rectangle.... | |
| University of Durham - Education, Higher - 1851
...Equal triangles upon the same base and upon the same side of it are between the same parallels. 4. **If a straight line be divided into any two parts, the square of the whole line is equal to the** square of the parts together with twice the rectangle contained by the parts. 5. To divide a given... | |
| 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... | |
| Education - 1863
...intercepted 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 - 1852
...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... | |
| Euclides - 1853
...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,...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... | |
| Euclides - Geometry - 1853 - 147 pages
...straight 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
...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... | |
| Euclid - Geometry - 1853 - 136 pages
...then (a) I. 46. (6 VI. 31. (c) Constr. (/) I. 34. a'2 = am -f- a n. PROPOSITION III. THEOREM. — If a **straight line (AB) be divided into any two parts (in C), the** rectangle under the whole line (AB) and one of those parts (CB) is equal in area to the square on that... | |
| Royal Military Academy, Woolwich - Mathematics - 1853
...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... | |
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