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" Iff 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... "
An elementary treatise on the geometrical and algebraical investigation of ... - Page 154
by Daniel Cresswell - 1817 - 436 pages
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The Elements of Euclid: The errors, by which Theon, or others, have long ago ...

Robert Simson, Euclid - Trigonometry - 1762 - 466 pages
...ftraight line, &c, Q^ED PROP. VIII. THEOR; TF a ftraight line be divided into any two parts, four times the rectangle contained by 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...
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The Elements of Euclid, viz: The errors, by which Theon, or others, have ...

Robert Simson, Euclid - Trigonometry - 1775 - 520 pages
...Q._E. D. cCof.4.t. E PROP. VIII. THEO K. TF a ftraight line be divided into any two parts, four times the rectangle contained by 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...
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Elements of algebra for the use of students in universities: to which is ...

William Trail - Mathematics - 1796 - 311 pages
...in place of that conftruction. PROP. PROP. I. To divide a given Jlraight line AB into two parts, fo that the rectangle contained by the -whole line, and one of the parts, may be equal to thefquare of the other part. This is Prop. i ith II. B. of Euclid. e ~-~ ACB Let C...
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The elements of Euclid: viz. the first six books, with the eleventh and ...

Alexander Ingram, Robert Simson - Trigonometry - 1799 - 351 pages
...34- 1• bCoi. 4. 2 PROP. VIII. TIIEOR. F a ftraight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the Iquare of the other part, is equal to the fquare of the ftraight line which is made...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - Euclid's Elements - 1803 - 279 pages
...fquareg of 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 - Trigonometry - 1804
...ftraight line, &c. Q^ED PROP. VIII. THE OR. IF a ftraight line be divided into any two parts, four times the rectangle contained by 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...
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Elements of geometry: containing the first six books of Euclid, with a ...

John Playfair - Trigonometry - 1806 - 311 pages
...the lines." ,, PROP. VIII. THEOR. .• 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, are equal to the square of the straight line which is made...
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Pantologia. A new (cabinet) cyclopędia, by J.M. Good, O. Gregory, and N ...

John Mason Good, Olinthus Gilbert Gregory - 1813
...of the other part. Prop. VIII. Theor. 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...
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclides - Geometry - 1816 - 528 pages
...straight line, &c. QED PROP. VIII. THEOfc. 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...
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Geometrical Problems Deducible from the First Six Books of Euclid: Arranged ...

Miles Bland - Geometry - 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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