 | 1867 - 336 pages
...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 - 222 pages
...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 - 382 pages
...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 - 830 pages
...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 - 152 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... | |
 | 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,...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 - 176 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 - 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... | |
 | Euclid - Geometry - 1853 - 176 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 - 400 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... | |
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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. 
