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

John Playfair - 1806 - 311 σελίδες
..." 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, are equal to the square of the straight line which is made up of the whole and the...

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

Robert Simson - 1806 - 518 σελίδες
...straight line, kc. QE D, PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1813
...and that part, together with the square of the other part. 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 equal to the square of the straight line which is made up of the whole and that...

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

Euclides - 1814
...with the square of AC. Wherefore, if a straight line, &c. QED 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 equal to the square of the straight line, which is'made up of the whole and that...

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

Euclides - 1816 - 528 σελίδες
...withthe square of AC. Wherefore, if a straight line, &c. QED PROP. VIII. THEOfc. 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...

An Elementary Treatise on the Geometrical and Algebraical Investigation of ...

Daniel Cresswell - 1817 - 436 σελίδες
...circle DPE. PROP. XXIV. 114. Problem. To divide a given finite straight line into two parts, such that the rectangle, contained by the whole line and one of the parts, shall most exceed the square of that part. Let AB be the given finite straight line ; it is required...

Pantologia. A new (cabinet) cyclopædia, by J.M. Good, O. Gregory ..., Τόμος 5

John Mason Good - 1819
...the square of the other part. Prop. \ III. Theor. If a straight line be divided into any two parto, 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 il made up of the whole and that...

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

John Playfair - 1819 - 317 σελίδες
...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 one 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...

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

John Playfair - 1819 - 333 σελίδες
...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, 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...

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

Miles Bland - 1819 - 377 σελίδες
...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,...




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