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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 first and second books of Euclid explained to beginners, by C.P. Mason - Page 152
by Euclid, Charles Peter Mason - 1872

Elements of geometry, containing the first two (third and fourth ..., Part 1

Euclides - 1871 - 136 pages
...BC and sq. on AC =sum of the eight rectangles and XH =AEFD = sq. on AD. X X 0 K Tf -U -XZ~ F p -R 0 If a straight line be divided into two equal, and...the squares on the two unequal parts are together double of the square an half the line and of the square on the line between the points of section....

The Edinburgh university calendar

Edinburgh univ - 1871 - 392 pages
...has 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...

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

Euclides, James Hamblin Smith - Geometry - 1872 - 376 pages
...of 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...the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section....

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

Henry Major - Student teachers - 1873 - 588 pages
...rectangle 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...

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...half the line, together with twice the square on the part between the points of section. Lot AB be a straight line, which is divided into two equal parts...

Recent Military, Naval, and Civil Service Examination Papers in Mathematics ...

Braithwaite Arnett - 1874 - 130 pages
...exterior 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...the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section....

A school Euclid, being books i. & ii. of Euclid's Elements, with notes by C ...

Euclides - 1874 - 120 pages
...than 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...the squares on the two unequal parts are together double of the square on half the line and of the square on the line between the points of section....

Pure mathematics, Volume 1

Edward Atkins - 1874 - 426 pages
...of 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...the squares on the two unequal parts are together double of the square on half the line, and of the square on the line between the points of section....