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" If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
A System of Popular Geometry: Containing in a Few Lessons So Much of the ... - Página xxxi
por George Darley - 1836 - 128 páginas
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - 1846 - 332 páginas
...multiplying both members of this equality by c, we shall have ac=ic+c2. PROP. IV. THEOR. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Let the straight...
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An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - 1847 - 358 páginas
...than in ordinary language. The proposition, (Euc. 4. 2.) that when a straight line is divided into two par.ts, the square of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonBtrated, by involving...
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The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848 - 52 páginas
...the two parts, together with the square of the aforesaid part. PROP. IV. THEOREM. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. COR. From the demonstration,...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

Jeremiah Day, James Bates Thomson - 1848 - 264 páginas
...concise, than in ordinary language. The proposition, (Euc 4. 2,) that when a straight line is divided into two parts, the square of the whole line is equal to the squares of the two parts, together with twice the product of the parts, is demonstrated, by involving...
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The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 120 páginas
...together with the square of BC. If therefore a straight, &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. Upon AB describe...
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Elements of Geometry and Conic Sections

Elias Loomis - 1849 - 252 páginas
...middle points of the sides which are not parallel. PROPOSITION VIII. THEOREM. If a straight line is divided into any two parts, the square of the whole line is equivalent to the squares of the two parts, together with twice the rectangle contained by 'the parts....
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Minutes ...: Correspondence, Financial Statements, Etc., and ..., Volumen2

Great Britain. Committee on Education - 1850 - 914 páginas
...makes the alternate angles equal. — Define parallel lines, and alternate angles. 3. If a line be cut into any two parts, the square of the whole line is equal to the squares of the parts, and twice the rectangle contained by the parts. — Show the same Algebraically....
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Papers for the Schoolmaster, Volumen2

1852
...triangle, and have one of its angles equal to * Riven rectilineal angle. SECTION II. 1. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the paits. 2. If a straight...
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University of Durham

University of Durham - 1851
...upon the same base and upon the same side of it are between the same parallels. 4. If a straight line be divided into any two parts, the square of the whole line is equal to the square of the parts together with twice the rectangle contained by the parts. 5. To divide a given...
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The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...by 7 is equal to 49. These added together make up 84.] BOOK n. PEOP. IV. THEOE. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts, Let the straight...
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