 | John Bonnycastle - 1803 - 306 pages
...AS, Bg, CD and DA. Q..ED PROP. XXII, PROBLEM. To divide a given right line into two parts, fo that the rectangle contained by the whole line and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given right line ; it is required to... | |
 | Robert Simson - Trigonometry - 1804 - 530 pages
...together with the fquare of AC. Wherefore if a ftraight line, &c. Q^ED PROP. VIII. THE OR. IF a ftraight line be divided into any two parts, four times the...whole line, and one of the parts, together with the fquare of the other part, is equal to the fquare of the ftraight line which is made up of the whole... | |
 | John Playfair - Mathematics - 1806 - 320 pages
...the lines together " with the square of the difference of the lines." ,, PROP. VIII. THEOR. .• IF a straight line be divided into any two parts, four...parts, together with the square of the other part, are equal to the square of the straight line which is made up of the whole and the firstmentioned part.... | |
 | John Mason Good - 1813 - 714 pages
...contained by the whole and that part, together with the square of the other part. Prop. VIII. Theor. If a straight line be divided into any two parts, four...equal to the square of the straight line which is made up of the whole and that part. Prop. IX. Theor. If a straight line be divided into two equal, and also... | |
 | Euclides - 1816 - 588 pages
...rectangleAB, BC, together withthe square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOfc. IF a straight line be divided into any two parts, four,...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 any two parts in the point... | |
 | Daniel Cresswell - Euclid's Elements - 1817 - 454 pages
...circle DPE. PROP. XXIV. 114. Problem. To divide a given finite straight line into two parts, such that the rectangle, contained by the whole line and one of the parts, shall most exceed the square of that part. Let AB be the given finite straight line ; it is required... | |
 | John Mason Good - 1819 - 800 pages
...the square of the other part. Prop. \ III. Theor. If a straight line be divided into any two parto, four times the rectangle contained by the whole line,...is equal to the square of the straight line which il made up of the whole and that part. double of the square of half the line, »na of tfc square nf... | |
 | John Playfair - 1819 - 354 pages
...difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts, fouf times the rectangle contained by the whole line, and...of the parts, together with the square of the other fart, is equal to the square of the straight line which is made up of the whole and the first-mentioned... | |
 | Miles Bland - Euclid's Elements - 1819 - 442 pages
...square of AC, ie to the square of the given line. (10.) To divide a given line into two such parts that the rectangle contained by the whole line and one of the parts may be (m) times the square of the other part, m being whole or fractional. Let AB be the given line,... | |
 | John Playfair - Circle-squaring - 1819 - 350 pages
...contained by the lines together with the •' square of the difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts , four times the reftanglt contained by the whole line, and one of the parts, together •with the square of the other... | |
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If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... 
