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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. "
The Elements of geometry [Euclid book 1-3] in general terms, with notes &c ... - Page 98
by Euclides - 1821
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United States Calculator: Or, Arithmetic Simplified

John M'Nevin - Arithmetic - 1841 - 300 pages
...2 x 10 = 20+ 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "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." Thus, let AB be...
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The United States Calculator: Or, Arithmetic Simplified, in Dollars and ...

John M'Nevin - Arithmetic - 1841 - 300 pages
...2 x 10= 20 + 2 = 2 tens and 2 over. Hence, from the properties of Euclid. 4, Lib. 2. "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." Thus, let AB be...
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The Mechanic's Calculator: Comprehending Principles, Rules, and Tables in ...

William Grier - Mechanical engineering - 1842 - 320 pages
...rectangles of AD and AE, and AD and EF, and AD and FB: thus expressed, AD . AB=AD . AE +AD . EF+AD . FB.* If a right line be divided into any two parts, the square of the whole line, is equal to both the rectangles of the whole line and each of the parts. 30. Let the line AB be the sum of any...
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Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...therefore, multiplying both members of this equality by c, we shall have ac= 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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Elements of geometry: consisting of the first four,and the sixth, books of ...

Euclides - 1842 - 316 pages
...together with the square of вc. If therefore a straight line, &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. Let the straight...
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Proceedings

Scotland free church, gen. assembly - 1847 - 554 pages
...angles. 3. Parallelograms upon equal bases, and between the same parallels, are equal. 4. If a straight line be divided into any two parts, the square of the whole line is equal to the squares of each of the parts together with twice the rectangle contained by the parts. 5. Equal straight...
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Elements of Algebra: Being an Abridgment of Day's Algebra, Adapted to the ...

James Bates Thomson - Algebra - 1844 - 266 pages
...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 Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 382 pages
...square of BC, together with the rectangle AC.CB.* If, therefore, &c. 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 their rectangle, t Let the straight line AB be divided...
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Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 218 pages
...with the square of BC. If therefore a straight line, &c. QED PROPOSITION IV. THEOB. — 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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Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845 - 546 pages
...square of BC. If therefore a straight line be divided, &c. QED PROPOSITION 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. Let the straight...
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