 | Euclid - 1845 - عدد الصفحات: 218
...PROPOSITION X. PROB. — To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. 14 t 24 Def. Constr. 4. 1. • 3. 1. t 1. 1. I Constr. || 24 Def. § 8. 1. 10 Def. \ D... | |
 | Euclid, James Thomson - 1845 - عدد الصفحات: 382
...which was to be done. PROP. XXX. PROB. — To divide a given straight line in extreme and mean ratio. Let AB be the given straight line ; it is required to divide it in extreme and mean ratio. Divide AB (II. 11 ) in the point C, so that the rectangle AB.BO may be equal... | |
 | Euclides - 1846 - عدد الصفحات: 292
...AC, CD. 'Wherefore, If a straight line %c. PROP. XI. PROII. To divide a yifen straight line into tioo parts, so that the rectangle contained by the whole...parts shall be equal to the square of the other part. Let AB be the given straight line : it is required to divide it into two parts, so that the rectangle... | |
 | Harvey Goodwin - 1846 - عدد الصفحات: 500
...(l + n) ' ma ' na n (a> + mx) = Ex. 5. Divide the quantity a into two parts such that the product of the whole and one of the parts shall be equal to the square of the other part. Let a? = one part ; .-. a- n' = the other; .-. by the question, ax = (a — at): = o2 - Zax + a?2,... | |
 | Euclid, John Playfair - 1846 - عدد الصفحات: 334
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide it into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the angle ACB... | |
 | 1847 - عدد الصفحات: 508
...angle contained by these two sides is a light angle. SECTION Il. — 1. To divide a straight line, so that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is less than the... | |
 | Great Britain. Committee on Education - 1847 - عدد الصفحات: 606
...the angle contained by these two sides is a right angle. SECTION II. 1. To divide a straight line, so that the rectangle contained by the whole and one...parts shall be equal to the square of the other part. 2. In every triangle the square of the side subtending either of the acute angles is less than the... | |
 | John Playfair - 1847 - عدد الصفحات: 340
...PROP. X. PROB. To bisect a given finite straight line, that is, to divide it into two equal parts. Let AB be the given straight line ; it is required to divide if into two equal parts. Describe (1. 1.) upon it an equilateral triangle ABC, and bisect (9. 1.) the... | |
 | Euclides - 1848 - عدد الصفحات: 52
...line made up of the half and the part produced. PROP. XI. PROBLEM. To divide a given straight line into two parts, so that the rectangle contained by...parts, shall be equal to the square of the other part. PROP. XII. THEOREM. In obtuse-angled triangles, if a perpendicular be drawn from either of the acute... | |
 | J. Goodall, W. Hammond - 1848 - عدد الصفحات: 390
...triangle between the perpendicular and the obtuse angle. Section 4. 1. Divide a given straight line into two parts, so that the rectangle contained by...parts shall be equal to the square of the other part. 2. Describe a square that shall be double a given triangle. 3. Prove that the diagonals of a parallelogram... | |
| |
AB be the given straight line ; it is required to divide it into two parts, so that the rectangle contained by the whole, and one of the parts, shall be equal to the square of the other part. 
