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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.
Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ... - Page 117
by Charles Reiner - 1837 - 215 pages

The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - Trigonometry - 1827 - 513 pages
...rectangle AC, CB, together with the square of BC. If therefore a straight line, &c. QED PROP. IV. THEOK. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C : the square of AB shall be equal to the...

An Introduction to Algebra: Being the First Part of a Course of Mathematics ...

Jeremiah Day - Algebra - 1827 - 332 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...squares of the two parts, together with twice the product of the parts, is demonstrated, by involving a binomial. Let the side of a square be represented...

Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - Geometry - 1829 - 186 pages
...equal to the rectangle contained by the two parts together with the square of the foresaid part. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the two parts. Or, in other words, the square of the sum of two lines is greater than the sum of their...

The Quarterly Journal of Education, Volume 5

Education - 1833
...equal to the rectangle contained by the two parts together with the square of the aforesaid part. 5. If a straight line be divided into any two parts, the...together, with twice the rectangle contained by the parts. a. Find the value of x in x1 — a x-\-b*^0. b. Divide a*— 3x*+x* + J x'-l'2x + 6 by ^-3. Find the...

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - 540 pages
...AC, CB together with the square of BC. " If, therefore, a straight line," &c. QED PROP. IV. THEOR. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Let the straight line AB be divided into any two parts in C; the square of AB is equal to the squares...

The Element of Geometry

John Playfair - Geometry - 1836 - 114 pages
...diagonal of any parallelogram, are equal so one another. Which was te be proved. PROP. XX. THEOR. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Let the straight line AB he divided into any two parts in C ; the square of AB is equal to the squares...

The Teacher's Assistant in the "Course of Mathematics Adapted to the Method ...

Mathematics - 1836 - 472 pages
...to the rectangle contained by the two parts, together with the square of the foresaid part. IV. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. Сок. From the demonstration, it is manifest that the parallelograms about the diameter of a square...

A System of Popular Geometry: Containing in a Few Lessons So Much of the ...

George Darley - Euclid's Elements - 1836 - 172 pages
...the rectangle under DE and CB, that is, the rectangle under AC and CB. This, &c. ART. 92. If a right line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the parts together with twice the rectangle under the parts. Let AB he a right...