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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 Elements of Euclid; viz. the first six books,together with the eleventh ... - Side 58
av Euclides - 1841 - 351 sider
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Minutes of the Committee of Council on Education

Great Britain. Committee on Education - 1853
...equal to the squares of the two parts, together with twice the rectangle contained by the parts. 2. If a straight line be divided into two equal and also...square of the line between the points of section. 3. If from any point without a circle two straight lines be drawn, one of which cuts the circle and...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1842 - 317 sider
...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...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts ; The squares of AD, DB are together...
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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842
...line. Wherefore, if a straight line, &c. QED PROP. IX. THEOR. equal parts are together equivalent to double of the square of half the line, and of the...points of section. Let the straight line AB be divided at the point c into two equal, and at D into two unequal parts : the squares of AD, DB are together...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - 1845 - 199 sider
...together in one straight line. Wherefore, if a straight line, &c. QED PROPOSITION IX. THEOR. — If a straight line be divided into two equal, and also...points of section. Let the straight line AB be divided at the point C into two equal, and at D into two unequal parts : the squares of AD, DB are together...
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The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1845 - 352 sider
...BC added 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 between...
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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...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 317 sider
...member of 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...points of section. Let the straight line AB be divided at the point C into two- equal, and at D into two unequal parts ; The squares of AD, DB are together...
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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...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...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...square of the line between the points of section. PROP. X. THEOREM. If a straight line be bisected, and produced to any point, the square of the whole...
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Solutions to the questions of the general examination at Easter, 1848 ...

J. Goodall, W. Hammond - 1848
...the square of the aforesaid part. 2. Prove that if a straight line be divided into two equal and also two unequal parts, the squares of the two unequal...square of the line between the points of section. 3. Prove that in obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles...
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