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COR. 1. Hence, because AD is the sum, and AC the difference of ' the lines AB and BC, four times the rectangle contained by any two lines, together with the square of their difference, is equal to the square ' of the sum of the lines." " COR. 2. From...
Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ... - Page 102
by Robert Mudie - 1836 - 496 pages

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Circle-squaring - 1819 - 350 pages
...AC the difference of " the lines AB and BC, four times the rectangle contained by any two •' lines together with the square of their difference, is equal to the " square of the sum of the lines." A E P D jsr o •' COR. 2. From the demonstration it is manifest, that since...

Popular Mathematics: Being the First Elements of Arithmetic, Algebra, and ...

Robert Mudie - Mathematics - 1836 - 542 pages
...difference of their squares. If we subtract the square of a — 6 from that of a +6, we have, 4ab — difference. Therefore, four times the product of any...whatever, of which the product is ab ; add to the factor COMPOUND PRODUCTS. 103 a, any quantity c, and the product becomes a 6+6 c; subtract any quantity c,...

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

Mathematics - 1836 - 488 pages
...and the first mentioned part. Сок. 1. Hence, four times the rectangle contained by any two lines together with the square of their difference, is equal to the square of the sum of the lines. 3. From the demonstration it is also manifest, that the square of any line is...

Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Euclid's Elements - 1837 - 332 pages
...and AC the difference of ' the lines AB and BC, four times the rectangle contained by any two lines, together with the square of their difference, is equal to the square ' of the sum of the lines." " COR. 2. From the demonstration it is manifest, that since the square ' of...

Elements of Plane Geometry According to Euclid

Andrew Bell, Robert Simson - Euclid's Elements - 1837 - 290 pages
...and AC the difference of the lines AB and BC, four times the rectangle contained by any two lines, together with the square of their difference, is equal to the square of the sum of the lines. Con. 2. — From the demonstration, it is manifest, that, since the square of...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...AC the difference of " the lines AB and BC, four times the rectangle contained by any two " lines, together with the square of their difference, is equal to the square " of the sum of the lines." " COR. 2. From the demonstration it is manifest, that since the square " of...

Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1846 - 334 pages
...AC the difference of " the lines AB and BC, four times the rectangle contained by any two " lines, together with the square of their difference, is equal to the square " of tht sum of the lines." . " COR. 2. From the demonstration it is manifest, that since the square " of...