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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... "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - Side 55
av Euclid, Robert Simson - 1821 - 516 sider
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - 1803 - 279 sider
...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...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1806 - 311 sider
...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....
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1813
...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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - 1816 - 528 sider
...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...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 436 sider
...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...
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Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Volum 5

John Mason Good - 1819
...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...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 sider
...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...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - 377 sider
...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,...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1819 - 333 sider
...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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