| Scotland free church, gen. assembly - 1847 - 552 pages
...other two sides, these sides contain a right angle. 3. Divide a given line into two parts, so that **the rectangle contained by the whole line and one of the parts** may be equal to the square of the other part. 4. The angle in a semicircle is a right angle. 5. Of... | |
| John Playfair - Euclid's Elements - 1844 - 338 pages
...also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight **line be divided into any two parts, four times the...one of the parts, together with the square of the** olher part, is equal to the square of the straight line which is made up of the whole and thefirst-mentioned... | |
| Euclid - Geometry - 1845 - 218 pages
...the square of AC. Wherefore, if a 'straight line, &c. QED PROPOSITION VIII. THEOR. — If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line, which is made of the whole and that part. Let the straight line AB be divided into any... | |
| Euclid, James Thomson - Geometry - 1845 - 380 pages
...of their difference, together with four tunes their rectangle. PROP. VIII. THEOR. — If a straight **line be divided into any two parts, four times the rectangle contained by the whole** and one of the parts, together with the square of the other part, is equal to the square of the straight... | |
| Euclides - 1845 - 544 pages
...nf, That is, If a number be divided into any two parts, four times the product of the whole number **and one of the parts, together with the square of the other part,** ig equal to the square of the number made up of the whole and that part. Prop. ix. Algebraically. Let... | |
| John Playfair - Euclid's Elements - 1846 - 332 pages
...also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line which is made up of the whole and the first-mentioned part. Let the straight line AB... | |
| Euclides - 1848 - 52 pages
...whole and that part, together with the square of the other part. PROP. VIII. THEOREM. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line, which is made up of the whole and that part. PROP. IX. THEOREM. If a straight line be... | |
| Euclid, Thomas Tate - 1849 - 120 pages
...together with the squares of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line which is made up of the whole and that part. Let the straight line AB be divided into... | |
| 1867 - 336 pages
...that the sum of the squares of two lines cannot be less than twice their rectangle. 3. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight liue which is made up of the whole and that part. Prove this also algebraically. SECTION VI.... | |
| Euclides - 1852 - 152 pages
...Proposition are equal to the two squares AE and kc added together.] PROP. VIII. THEOR. If a straight **line be divided into any two parts, four times the...square of the other part, is equal to the square of the** straight line, which is made up of the whole and that part. [This Proposition may advantageously be... | |
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