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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 on the other part, is equal to the square on the straight line which is made up of the whole and that... "
Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ... - Page 85
by John Mason Good - 1813
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - Trigonometry - 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 - Euclid's Elements - 1806 - 311 pages
...the rectangle contained by the lines together " with the square of the difference of the lines." ,, PROP. VIII. THEOR. .• IF a straight line be divided...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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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Trigonometry - 1806 - 518 pages
...twice the rectangle AB, BC, together with the square of AC. Wherefore, if a straight line, kc. QE D, PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour times the rectangle contained by the whole line, and one of the parts, together with the square...
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An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - Euclid's Elements - 1817 - 436 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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 333 pages
...the rectangle 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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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...twioe the rectangle 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, fouf times the rectangle contained by the whole line, and one of the parts, together with the square...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 377 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,...
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 377 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,...
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Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...THEOREM. I/* a rig A/ /ѓие iе аиу how ait into two parts, four times the rectangle, contained under the whole line, and one of the parts, together with...square of the other part, is equal to the square of the line, compounded of the whole line, and the first part taken as one line. Let the right line AB be...
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Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 180 pages
...THEOREM. If a right line be any how ait into two parts, four times tlie rectangle, contained under (he whole line, and one of the parts, together with the...square of the other part, is equal to the square of the line, compounded of the whole line, and the first part taken as one line. Let the right line AB be...
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