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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.
First Steps in Geometry: A Series of Hints for the Solution of Geometrical ... - Page 175
by Richard Anthony Proctor - 1887 - 180 pages

## The first and second books of Euclid explained to beginners, by C.P. Mason

Euclid, Charles Peter MASON - Geometry - 1872 - 216 pages
...square 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...

## Elements of geometry, containing books i. to vi.and portions of books xi ...

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...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...

## The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - Student teachers - 1873 - 592 pages
...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...

## Elements of Euclid Adapted to Modern Methods in Geometry

Euclid, James Bryce, David Munn (F.R.S.E.) - Geometry - 1874 - 236 pages
...by four times their rectangle" (cor. to Prop. 7). PROP. IX.— THEOREM. (Euc. II. 9.) ij a slraic/ht line be divided into two equal, and also into two unequal parts, the squares on the two unequal parts are together equal to twice the square on half the line, together with twice...

## Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...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...

## Recent military, naval, and civil service examination papers in mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...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...

## A School Euclid. Being Books I.&II. of Euclid's Elements. With Notes ...

Euclides - 1874 - 120 pages
...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...

## The Elements of Euclid, containing the first six books, with a selection of ...

Euclides - 1874 - 342 pages
...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...