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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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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

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...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 - 1825 - 372 σελίδες
...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 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 that...

The Principles of Analytical Geometry: Designed for the Use of Students

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...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,...

Euclid's Elements of geometry, transl. To which are added, algebraic ...

Euclides - 1826
...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 the square of the other part, is equal to the square of the line, compounded of the whole line, and the first...

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

Robert Simson - 1827 - 513 σελίδες
...the square of AC. Wherefore if a straight line, 8cc. QED G PROP. VIII. THEOR. If a straight line he 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 that...

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

John Playfair - 1829 - 186 σελίδες
...together equal to the square of the whole line. ..If a straight line be divided into any two parts, the rectangle contained by the whole line and one of the parts is equal to the rectangle contained by the two parts together with the square of the foresaid part....

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

John Playfair - 1832 - 333 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 I he parts? together with thesquare of the other part, is equal to the square of the straight line...

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

John Playfair - 1833 - 333 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...line, and one of the parts, together with the square of the other part, is equalto the square of the straight line which is made up of the whole and the...

The Elements of Euclid; viz. the first six books, together with the eleventh ...

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...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 part. BOOK II. PROP. VIII. Let the straight Iine AB be divided into any two parts in the point C : four times...

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

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...Wherefore, " if a straight line," &c. QED PROP. VIII. THEOR. JJ F E a 34. 1. 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 t/ie other part, is equal to the square of the straight line which is made up of the whole and that...




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