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" IF a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts are together double of the square of half the line, and of the square of the line between the points of section. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 58
by Euclides - 1841
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The Edinburgh university calendar

Edinburgh univ - 1871 - 392 pages
...the greater angle is greater than the base of the other. A complete demonstration is required. 4. If a straight line be divided into two equal, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of...
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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
...the eight rectangles and XH =AEFD — sq. on AD. QED JC G ^ V 0 JT j> it PROPOSITION IX. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the...
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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
...on the hypotenuse is equal to the sum of the squares on the other two sides. (I. 47.) 2. That if a line be divided into two equal, and also into two unequal parts, the rectangle contained by the unequal parts together with the square on the part between the points of...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 592 pages
...AC, CB. Coa. The parallelograms about the diameter of it square, are likewise squares. ,7\ V. — If a straight line be divided into two equal, and also into two unequal parts ; the rectangle contained by the unequal parts, together with the square of the line between the points of...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 428 pages
...the two unequal parts are together double of the square on half the line, and of the square on tlie line between the points of section. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts in the point D ; The squares on AD and DB shall be together...
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The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...together in one straight line. Wherefore, if a straight line, &c. QED PROPOSITION 9. — Theorem. If a straight line be divided into two equal, and also into two unequal parts, the squares cm the two unequal parts are together double of the square on half the line, and of the square on the...
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A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 pages
...the square on the sum of the two lines by the square on their difference. PROPOSITION 9. THEOREM. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line and of the square on the...
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Pure mathematics, Volume 1

Edward Atkins - 1874 - 424 pages
...AB and BC together. (AB+BC>. Therefore, if a straight line, &c. QED Proposition 9. — Theorem. If a straight line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the...
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Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...angle is equal to the two interior and opposite angles. Trisect a given finite straight line. 3. If a straight line be divided into two equal and also into two unequal parts, the squares on the two unequal parts are together double of the square on half the line, and of the square on the...
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The Examination papers set for the preliminary examination of candidates for ...

Royal College of Surgeons of England - 1874 - 34 pages
...angles ; and the three interior angles of any triangle are together equal to two right angles. 7. If a straight line be divided into two equal, and also into two unequal parts, the rectangle contained by the unequal parts, together with the square of the line between the points of...
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