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 ...

Euclid, John Playfair - Circle-squaring - 1819 - 348 pages
...lines." PROP. VIII. THEOR. If a straight line be divided into any two parts , four times the reftanglt contained by the whole line, and one of the parts,...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... ## Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - 317 pages
...difference of the lines." PROP. VIII. THEOR. If a straight line be divided into any two parts, fouf times the rectangle contained by the whole line, and...of the parts, together with the square of the other fart, is equal to the square of the straight line which is made up of the whole and the first-mentioned... ## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 442 pages
...square of AC, ie to the square of the given line. (10.) To divide a given line into two such parts that the rectangle contained by the whole line and one of the parts may be (m) times the square of the other part, m being whole or fractional. Let AB be the given line,... ## Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - Euclid's Elements - 1819 - 444 pages
...square of AC, ie to the square of the given line. (10.) To divide a given line into two such parts that the rectangle contained by the whole line and one of the parts may be (m) times the square of the other part, m being whole or fractional. Let AB be the given line,... ## A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - Mathematics - 1825 - 372 pages
...square ot AC. Wherefore, if a straight line, &c. QED | ¿J J'rojjosiiion VIII. Theorem. 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 that part. Let the straight line AB be divided into... ## Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826 - 226 pages
...THEOREM. I/* a rig A/ /ѓие iе аиу how ait into two parts, four times the rectangle, contained under the whole line, and one of the parts, together with...square of the other part, is equal to the square of the line, compounded of the whole line, and the first part taken as one line. Let the right line AB be... ## Elements of Geometry, Containing the First Six Books of Euclid

Euclid - 1826 - 236 pages
...THEOREM. If a right line be any how ait into two parts, four times tlie rectangle, contained under (he whole line, and one of the parts, together with the...square of the other part, is equal to the square of the line, compounded of the whole line, and the first part taken as one line. Let the right line AB be... ## The Principles of Analytical Geometry ...

Henry Parr Hamilton - Geometry, Analytic - 1826 - 326 pages
...solutions. For example, if it be required to divide a given straight line into two such parts, that the rectangle contained by the whole line and one of the parts, shall be equal to the square of the other part; this problem is determinate. If on the other hand,... ## Elements of Geometry: Containing the First Six Books of Euclid, with a ...

Euclid, John Playfair - Euclid's Elements - 1826 - 326 pages
...line be divided into any two parts, four times the reetangle eontained by the whole line, arid ohtt of the parts, together with the square of the other part> iS H equal to the square of the straight line whieh is made up of the whole and the first-mentioned part.... 