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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... "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 86
by Euclides - 1871
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 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,...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 part....
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The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter Mason - Geometry - 1872 - 216 pages
...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 - 588 pages
...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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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...together with the square on AC. Therefore, if a straight line, &c. QED Proposition 8. — Theorem. If a straight line be divided into any two parts,...contained by the whole line and one of the parts, toget/ier with the square on the other part, is equal to the square on tlie straight line which is...
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A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874 - 120 pages
...line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced. j Let the straight line AB he hisected at the point ' • C, and produced...
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Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced. 4. If a straight line drawn through the centre of a circle bisect a straight...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line, and one of the parts, shall be equal to the square on the other part. Construction. Upon AB describe the square ACDB (I....
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Euclidian Geometry

Francis Cuthbertson - Euclid's Elements - 1874 - 400 pages
...rectangle BP, PQ + rectangle BP, QC. Hence, if a straight line be divided into any number of parts, the rectangle contained by the whole line and one of the parts is equal to the square on that part together with the rectangles contained by that part and the other...
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Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...BC. <^. E. D, PROP. III. — THEOREM. (Euc. II. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, is equal to the square of that part, together with the rectangle contained by the two parts. Let AB...
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Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1876 - 376 pages
...be drawn from G to B and from (f to D, shew that BO D ia a straight line. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle contained by ike whole line and one of the parts, together with the square on the other part, is equal to the square...
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