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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 for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...straight line &c. QED B t> PROPOSITION 8. THEOREM. If a straight line be divided into any two parti, four times the rectangle contained by the whole line and one of the parts, together with the square en the other part, is equal to the square on the straight line which is made up of the whole and that...
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The Elements of Euclid for the Use of Schools and Colleges: Comprising the ...

Euclid, Isaac Todhunter - Euclid's Elements - 1867 - 400 pages
...BC, together with the square on AC. Wherefore, if a straight line &c. QED A PROPOSITION 8. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained l)ij the whole line and one of the parts, together with the square en the other part, is equal to the...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1868 - 410 pages
...BC, together with the square on AC. Wherefore, if a straight line, &c. QED PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts,...four times the rectangle contained by the whole line, mid one of the parts, together with the square un the other part, is equal to the square on tlte straight...
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Elementary geometry

James Maurice Wilson - 1869
...by addition that AB* + BC* = 2AD* + 2DB*. Ex. 3. To divide a straight line into two parts such that the rectangle contained by the whole line and one of the parts is equal to the square of the other part. Let AB be the given line. Construction. Draw a square ACDB...
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1870
...arithmetical progression; as 324, 1G4, and 4, — the com. dif. being 160. PROP. 8. — THEOR. If a st. line be divided into any two parts, four times the...together with the square of the other part, is equal to tlie square of the st. line which is made up of the whole and that part. Coxs. — Pst. 2. A terminated...
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Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871
...If straight lines be drawn from G to B and from G to Z>, shew that BGD is a straight line. /i as a If. a straight line be divided into any two parts,...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 the...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 349 pages
...be drawn from G to B and from G to D, show that BGD is a straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts,...line and one of the parts, together with the square on the otJter part, is equal to the square on the straight line which is made up of the \ and the first...
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872
...whole line BC and each of its parts. PBOPOSITION III. If a right line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangle contained by the two parts. The propositions...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873
...squares of A] ! and BC are equal to twice the rectangle AB, BC. together with the square of AC. VIII. — If a straight line be divided into any two parts four times the rectangle contained by the wJwle line, and one of the parts, together with the square oftha other part, is equal to the square...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874
...proposition in Algebra is similarly expressed, and is thus represented in symbols, PROPOSITION 8. THEOREM. If a straight line be divided into any two parts,...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...
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