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" 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 line between the points of section. "
Elements of Euclid Adapted to Modern Methods in Geometry - Page 87
by Euclid, James Bryce, David Munn (F.R.S.E.) - 1874 - 216 pages
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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...is one straight line. Wherefore, if a straight line, &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...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...together in one straight line. Therefore, 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...
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The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846 - 292 pages
...the rectangle ABCD is equal to twice the triangle AEF together with the rectangle BE, DF. 21. If a line be divided into two equal and also into, two unequal parts, the squares of the two unequal parts are together equal to twice the rectangle contained by these parts together...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...this equality, we shall have, 4aJ+c2=c2+4ic+4J2, or4ai+c2=(c4-26)2. 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...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 pages
...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...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 pages
...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...
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Papers for the Schoolmaster, Volume 2

1852 - 316 pages
...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...
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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...
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The first two books of the Elements of Euclid, with additional figures ...

Euclides - 1852 - 152 pages
...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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...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...
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