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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 Geometry: Containing the First Six Books of Euclid, with a ... - Σελίδα 55
των Euclid, John Playfair - 1826 - 320 σελίδες
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Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - 1837 - 318 σελίδες
...and adding c2 to each member of this equality, we shall have, 4aJ+c2=c2+4ic+4*2, or4ai+c2=(c-|-2i)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also into twn unequal parts ; the squares of the two unequal parts are together double of the square of half...

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...A!), that is, of AB 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...the squares of the two unequal parts are together doable of the square of half the line, and of the square of the line between the points of section....

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 σελίδες
...and adding c2 to each member of this equality, we shall have, 4ai+c2=c2+4ic+462, or 4ai+c2=(cr-26)2. PROP. IX. THEOR. If a straight line be divided into two equal, and also into twn unequal parts ; the squares of the two unequal parts are together double of the square of half...

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

Euclid, James Thomson - 1845 - 352 σελίδες
...and AD is equal to AB and BC added together in one straight line. Therefore, if a straight line, &c. PROP. IX. THEOR. — If a straight line be divided...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 between...

Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...lines is never less than twice their rectangle. 8. If a straight line be divided into two equal and into two unequal parts, the squares of the two unequal parts are equal to twice the rectangle contained by the two unequal parts, together with four times the square...

The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...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...the squares of the two unequal parts are together equal to twice the rectangle contained by these parts together with four times the square of the line...

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

Upper Canada. Chief Superintendent of Schools - 1854
...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 line between...

Orr's Circle of the Sciences: The mathematical sciences

William Somerville Orr - 1854
...straight line (AB) be divided into two equal, and also into two unequal parís (in С and D), tlie squares of the two unequal parts are together double of the square of half the line (AC), and of the square of the Km (GD), between the points of section : that is, A D+ DB= = twiee AC?...

The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856
...manifest that the rectangles about the diameter of a square are likewise squares. L. — EUCLID II. 5. 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...

Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856
...If the square on the hypothenuse be fire times that on one of the sides; compare the two sides. 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...




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