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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 Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1826 - 326 pages
.../ P R C. Now BO+RC.AC=\B.BC (3.2.) and therefore AD3==AC + 4\B.BC. Q, E, D," -V PROP. IX. THEOR. ., 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 Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 546 pages
...and BC added together in one straight line. Wherefore, if a straight line, &c. GED PROP. IX. THEOR. If a straight line be divided into two equal, and also into two unequal parts; the squares of the two unequal parts arc together double of the square of half the line, and of the square of the...

## Dialogues on the First Principles of the Newtonian System, Volume 4

Walter Henry Burton - Astronomy - 1828 - 84 pages
...you will understand this proposi-Prop. xix. tion, which is necessary for our further progress: that if a straight line be divided into two equal, and also into two unequal parts, the square of either of the equal parts (or the rectangle under both) is equal to the rectangle under the...

## A Collection of Cambridge Mathematical Examination Papers: Papers in the ...

John Martin Frederick Wright - Astronomy - 1831 - 282 pages
...side subtending the right angle, is equal to the square on the sides containing the right angle. 7. If a straight line be divided into two equal, and also into two unequal parts, prove that the squares of the two unequal parts are, together, double of the square of half the line,...

## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...straight line. Wherefore, " if a straight line" &c. QED HL A. M X CB D / G K M 0 P / R / PROP. IX. THEOR. 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...

## The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 488 pages
...demonstration it is also manifest, that the square of any line is quadruple of the square of half that line. IX. 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...

## Solutions of the Cambridge Problems, from 1800 to 1820, Volume 2

John Martin Frederick Wright - Mathematics - 1836 - 776 pages
...parallelogram equal to a given rectilinear figure, having an angle equal to a given rectilinear angle. 2. 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...

## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1837 - 410 pages
...AB and BC added together in one straight line. * Wherefore, if a straight line, &c. PROP. IX. THEOR. IF a straight line be divided into two equal, and also into two unequal parts ; the squares of the unequal parts are together double of the square of half the line, and of the square of the line...