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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

## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclid - 1848 - 52 pages
...to the square of the straight line, which is made up of the whole and that part. PROP. IX. THEOREM. 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 three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...and BC added together in one straight line. Wherefore, if a straight line, &c. QED 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...

## Papers for the Schoolmaster, Volume 2

1852 - 314 pages
...equal to the squares of the two parts, together with twice the rectangle contained by the paits. 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...

## Papers for the schoolmaster, Volume 3

1867 - 336 pages
...up of the whole and that part. Prove this also algebraically. SECTION VI. 1. If a str tight line he 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 two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...that is, of AB and BC added together in one straight line. H X G T / K / / R BOOK II. 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 geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...added together in one straight line. Wherefore, if a straight line, etc. QED PROPOSITION 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 synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853 - 146 pages
...and BC added together in one straight line. Wherefore, if a straight line, &c. QED PROP. IX. THEOREM. 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 books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 176 pages
...added together in one straight line. Wherefore, if a straight Une, &c. QED PROPOSITION IX. — THEOREM. 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...

## Annual Report of the Normal, Model, and Common Schools in Upper Canada for ...

Upper Canada. Chief Superintendent of Schools - Education - 1854 - 196 pages
...of the whole line is equal to the squares of the two parts, together with twice their rectangle. 4. 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 squares of half the line, and of the squares of the...

## Liber Cantabrigiensis, an account of the aids afforded to poor students, the ...

Robert Potts - 1855 - 1050 pages
...triangle be produced, the exterior angle is greater than either of the interior opposite angles. 12. 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...