| Euclides - 1856 - 168 pages
...1. — By making A equal to the whole line considered as divided into two parts, it appears that if **a straight line be divided into any two parts, the square of the whole** liriiHs equal to the sum of the rectangles contained by the whole line and each of the parts. Cor.... | |
| Great Britain. Parliament. House of Commons - Bills, Legislative - 1858 - 690 pages
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** 6. PROP. IX. — If a straight line be divided into two equal, and also into two unequal parts ; the... | |
| 1858 - 398 pages
...the sides is bisected in that point, and also bisects the parallelogram. BOOK II. 5. PROP. IV. — If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** 6. PROP. IX. — If a straight line be divided into two equal, and also into two unequal parts ; the... | |
| War office - 1858 - 578 pages
...vertical angle of the triangle and the point of intersection will bisect the vertical angle. 4. If **a straight line be divided into any two parts, the...square of the whole line is equal to the squares of the** parts and to twice the rectangle contained by the parts. Explain how a rectangle is represented arithmetically,... | |
| Elias Loomis - Conic sections - 1858 - 256 pages
...THEOREM. If a straight line is divided into any two parts, the square oj the whole line is equivalent **to the 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 square on AB is equivalent to the... | |
| Euclides - 1858 - 248 pages
...parallelogram which are about the diameter of any parallelogram, are equal to one another. 4. II. If a st. **line be divided into any two parts, the square of the whole line** equals the square of the two parts together with twice the rectangle contained by the parts. Def. 30.... | |
| Euclides - 1858 - 134 pages
...I, Ax. 1. Hyp. Cone. •ui Con e. Def. 1.1 1. .in. I. \x. I. BOOK II. 85 PROP. IV. THEOII. If a st. **line be divided into any two parts, the square of the whole line** equals the squares of the two parts, together with twice the rectangle contained by the parts. CоN.... | |
| Sandhurst roy. military coll - 1859 - 672 pages
...the following equations ,-, 2x + 5 5 2x-5 3 2.a? + 7 2j;-7 __ 1^ ~ 14 21 1 (2) bx-ay=d EUCLID. 1. If **a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts.** 2. In every acute-angled triangle the square of the side subtending either of the acute angles is less... | |
| Thomas Stantial - Examinations - 1859 - 356 pages
...the features of "parallel lines" and "parallelograms" gained from the first book of Euclid. 3. " If **a straight line be divided into any two parts, the square of the whole line is equal to the** rectangles contained by the whole and each part." Prove this (1) by geometry ; (2) by algebraic demonstration... | |
| Civil service - 366 pages
...bisected in that point, and also bisects the parallelogram. BOOK II. PROP. IV — If a straight lice **be divided into any two parts, the square of the whole...together with twice the rectangle contained by the parts.** PROP. IX. — If a straight line be divided into two equal, and also into two nnequal parts ; the squares... | |
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