Books Books 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... Gradations in Euclid : books i. and ii., with an explanatory preface [&c ... - Page 161
by Euclides - 1858 ## Elements of Geometry: Containing the First Six Books of Euclid : with a ...

John Playfair - Geometry - 1837 - 332 pages
...also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the...square of the other part, is equal to the square of the straight line which is made up of the whole and the first-mentioned part. Let the straight line AB... ## The First Six and the Eleventh and Twelfth Books of Euclid's Elements: With ...

Euclid - Geometry - 1837 - 410 pages
...square of 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 - Geometry - 1837 - 254 pages
...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.... ## The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - Geometry - 1838 - 434 pages
...together with the square AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. Ir a straight line be divided into any two parts, four times the...square of the other part, is equal to the square of the straight line which is made up of the whole and that part. Let the straight line AB be divided into... ## Euclid's Elements [book 1-6] with corrections, by J.R. Young

Euclides - 1838 - 264 pages
...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...square of the other part, is equal to the square of the straight line, which is made up of the whole and that part. Let the straight line AB be divided into... ## The figures of Euclid with the enunciations, as printed in Euclid's Elements ...

Euclides - 1840 - 82 pages
...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 - 194 pages
...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 ;... ## The Elements of Euclid; viz. the first six books,together with the eleventh ...

Euclides - 1841 - 378 pages
...together with the square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOR. Iff a straight line be divided into any two parts, four times the...square of the other part, is equal to the square of the straight line which is made up of the whole and that part. Let the straight line AB be divided into... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

John Playfair - Euclid's Elements - 1842 - 332 pages
...also derived from the above algebraical equality, by transposition. PROP. VIII. THEOR. If a straight line be divided into any two parts, four times the...square of the other part, is equal to the square of the straight line which is made up of the whole and the first-mentioned part. Let the straight line AB... 