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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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The geometry of the circle and mathematics as applied to geometry by ...

James Smith - 1869 - 470 páginas
...area of a rectangle of which AD and AE are sides. By Euclid : Prop. 2 : Book 2 : " IJ -a straight line be divided into any two parts, the square of the whole line is equal to the sum of the rectangles contained by the whole line and tach of its parts" Hence :(AD-AE + AD.ED) = AD', that is,...
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Civil service guide

Robert Johnston (F.R.G.S.) - 1869 - 178 páginas
...proved that the three angles of a triangle are together equal to two right angles. 4. 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. 5. Divide a given...
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The ratio between diameter and circumference in a circle demonstrated by ...

James Smith - 1870
...Now, by Euclid : Prop. 2 : Book 2 : '' If a straight line (AB) be divided into any two parts (AC, CB), the square of the whole line is equal to the sum of the rectangles contained by the whole line and each of its parts :" and I shall proceed to prove that this...
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The Elements of Plane and Solid Geometry

Henry William Watson - 1871 - 285 páginas
...twice the rectangle of one of the lines and half the other line. PROPOSITION 12. If a straight line be divided into any two parts, the square of the whole line shall be equal to the sum of the squares of the two parts, together with twice the rectangle of those...
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The Acting Teacher's and Student's in Training Guide and Text Book for ...

Henry Major - 1873
...rectangle AB, BC, is equal to the rectangle AC, CB, together with the square of BC. -If a straiyht 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 "tarts. ca Let AB be divided...
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Pure mathematics, Volumen1

Edward Atkins - 1874
...11. If a straight line be divided into any number of parts, the square of the whole line is equal to the sum of the squares of the parts, together with twice the rectangles of the parts taken two and two together. 12. If ABC be an isosceles triangle, and DE be...
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Elements of geometry, based on Euclid, books i-iii

Edward Atkins - 1876 - 119 páginas
...tho rectangle under the extreme segments. • 11. If a straight line be divided into any number of parts, the square of the whole line is equal to the sum of the squares of tho parts, together with twice the rectangles of the parts taken two and two together. 12....
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Elements of Geometry, Conic Sections, and Plane Trigonometry

Elias Loomis - 1877 - 458 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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Elements of Plane Geometry, Parte1

Thomas Hunter - 1878 - 142 páginas
...because AB=BD. Therefore AB"=AB. AC+AB.CB. PROPOSITION XVI.—THEOREM. If a straight line be divided into two parts, the square of the whole line is equal to the sum of the squares of the parts and twice the rectangle contained by the parts. Let AB be a straight line divided...
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The Elements of Plane and Solid Geometry: With Chapters on Mensuration and ...

Isaac Sharpless - 1879 - 282 páginas
...AB.BE=AB.BC; AD-AC.CD = AC.CB, CE= CB\ AB.BC-AC.CB+CB\ Proposition 4. 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 two part*. Let the straight...
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