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" If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... "
The Elements of Euclid for the Use of Schools and Colleges: Comprising the ... - Σελίδα 60
των Euclid, Isaac Todhunter - 1883 - 400 σελίδες
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Library of Useful Knowledge: Geometry, plane, solid, and spherical [by ...

1835
...square of the whole une. PROP. 31. (Eue. ii. 3.) If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts, shall be equal to the rectangle contained by the two parts, together with the square of the aforesaid...

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

1836 - 472 σελίδες
...contained by the lines together with the square of the difference of the lines. VIII. If a straight line be divided into any two parts, four times the rectangle...line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and the...

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

John Playfair - 1836 - 471 σελίδες
...together with the square of the difference of the " lines." PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the rectangle...contained by the whole line, and one of the parts, togetiier with the square of the other part, is equal to the square of the straight line which is made...

Elements of Plane Geometry According to Euclid

Andrew Bell - 1837 - 240 σελίδες
...the rectangle AB-BC, together with the square of AC. PROPOSITION VIII. THEOREM. If a straight line be divided into any two parts, four times the rectangle...line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and the...

A companion to Euclid: being a help to the understanding and remembering of ...

Euclides - 1837 - 88 σελίδες
...2 AH + KF ; ;and that these = 2 AB x BC + AC*. CBD PROPOSITION VIII. Theorem. If a straight line be divided into any two parts, four times the rectangle...line and one of the parts, together with the square of the other part, is equal to the square of the line made up of the whole and that part. R In the...

The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid, James Thomson - 1837 - 390 σελίδες
...their difference, together with four times their rectangle. PROP. VIII. THEOR. IF a straight line be divided into any two parts, four times the rectangle contained by the whole and one of the parts, together with the square of the other part, is equal to the square of the straight...

Lessons on Form: Or, An Introduction to Geometry, as Given in a Pestalozzian ...

Charles Reiner - 1837 - 215 σελίδες
...a c. M.—Express this truth in words. P.—If a straight line be divided into any two parts, twice the rectangle contained by the whole line and one of the parts is equal to twice the square upon that part, together with twice the rectangle contained by the parts....

Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838
...AC. Wherefore, if a straight line, &c. t>. i:. i,. * PROP. VIII. THEOR. If a straight line be dieided into any two parts, four times the rectangle contained...line and one of the parts, together with the square of the other part, is equal to the square of the straight line, which is made up of the whole and that...

The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840
...and the produced part. .n. . PROP. XI. PROB. To divide a given straight line in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. rtl PROP. XII. THEOR. In an obtuse-angled triangle, the...

Euclid's Elements of plane geometry [book 1-6] with explanatory appendix ...

Euclides - 1840
...half and the produced part. PROP. XI. PROB. To divide a given straight line (AB) in such a manner that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. Upon AB construct the square ACDB ; bisect AC in E ;...




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