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 Books Books 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 Euclid; viz. the first six books, together with the eleventh ... - Page 45
by Euclides - 1814
Full view - About this book ## The First Six, and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - Geometry - 1845 - 352 pages
...equal to the 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 squares of the two parts, together with twice their rectangle, t Let the straight line AB be divided into any two parts in C ; the square of AB is...
Full view - About this book ## Euclid's Elements of geometry [book 1-6, 11,12] with explanatory notes ...

Euclides - 1845
...line is equal to four times the square of half the line. Also, if a line be divided into any three parts, the square of the whole line is equal to the squares of the three parts, and twice the rectangle contained by every two parts. Prop. iv. Algebraically, (fig. Prop,...
Full view - About this book ## A system of practical mathematics; being no.xvi. of a new series of school-books

...two parts in the point C, the proposition becomes the following. 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, together with twice the rectangle contained by the parts. Cor. 2....
Full view - About this book ## Euclid in Paragraphs: The Elements of Euclid: Containing the First Six Books ...

Euclid - Geometry - 1845 - 199 pages
...twice the rectangle contained by the whole and that part, together with the square of the other part. Let the straight line AB be divided into any two parts in the point C ; the squares of AB, BC are equal to twice the rectangle AB, BC, together with the square...
Full view - About this book ## Euclid's Elements of geometry, the first three books (the fourth, fifth, and ...

Euclides - 1846
...under AC and CF. PROPOSITION IV. THEOREM. If a right line (AB) be divided into any two parts, (in O) the square of the whole line is equal to the squares of the parts, together with twice the rectangle under the parts. On AB describe the square ACDB, and draw...
Full view - About this book ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 317 pages
...contained by the whole and each of the parts, are together equal to the square of the whole line. c B Let the straight line AB be divided into any two parts in the point C ; the rectangle AB.BC, together with the rectangle AB.AC, is equal to the square of AB...
Full view - About this book ## The Elements of Euclid, the parts read in the University of Cambridge [book ...

Euclides - 1846
...equal to the rectangle contained by the two parts, together with the square of the aforesaid part, Let the straight line AB be divided into any two parts in the point C : the rectangle AB, BC shall be equal to the rectangle AC, CB, together with the square...
Full view - About this book ## An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1847 - 332 pages
...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...squares of the two parts, together with twice the product of the parts, is demonBtrated, by involving a binomial Let the side of a square be represented...
Full view - About this book ## Minutes of the Committee of Council on Education, Volume 2

...triangle. 3. A straight line being divided into two parts, prove the square of the whole line to be equal to the squares of the two parts, together with twice the rectangle contained by the parts. 4. Prove the angle in a semicircle to be a right angle. 518 mities 36° 201 and 60° 10* ; required...
Full view - About this book ## The definitions, postulates, axioms, and enunciations of the propositions of ...

Euclides - 1848
...rectangle contained by the two parts, together with the square of the aforesaid part. PROP. IV. THEOREM. If a straight line be divided into any two parts,...together with twice the rectangle contained by the parts. COR. From the demonstration, it is manifest, that the parallelograms about the diameter of a square...
Full view - About this book