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" Iff 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... "
An Elementary Treatise on the Geometrical and Algebraical Investigation of ... - Strona 154
autor: Daniel Cresswell - 1817 - Liczba stron: 436
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Geometrical Problems Deducible from the First Six Books of Euclid, Arranged ...

Miles Bland - 1819 - Liczba stron: 377
...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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A Supplement to the Elements of Euclid

Daniel Cresswell - 1819 - Liczba stron: 410
...proportional to the parts of them, between the given point and the convex circumference. PROP. L. 59. PROBLEM. To divide a given finite straight line into two parts, such, that another given straight line, not greater than the half of the former, shall be a mean proportional...
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Elements of Geometry: Containing the First Six Books of Euclid: With a ...

John Playfair - 1819 - Liczba stron: 317
...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...
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A Popular Course of Pure and Mixed Mathematics ...: With Tables of ...

Peter Nicholson - 1825 - Liczba stron: 372
...QED | ¿J J'rojjosiiion VIII. Theorem. 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...
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A Supplement to the Elements of Euclid

Daniel Cresswell - 1825 - Liczba stron: 582
...reciprocally proportional to the parts of them between the given point and the convex circumference. L. PR. To divide a given finite straight line into two parts such that another given straight line, not greater than the half of the former, shall be a mean proportional...
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The Principles of Analytical Geometry: Designed for the Use of Students

Henry Parr Hamilton - 1826 - Liczba stron: 326
...number of 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, it were...
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The Elements of Euclid: The Errors by which Theon, Or Others, Have Long ...

Robert Simson - 1827 - Liczba stron: 513
...straight line, 8cc. QED G PROP. VIII. THEOR. If a straight line he 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...
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Elements of Geometry: Being Chiefly a Selection from Playfair's Geometry

John Playfair - 1829 - Liczba stron: 186
...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....
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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 part....
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The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ...

Euclid - 1835 - Liczba stron: 513
...QED PROP. VIII. THEOR. JJ F E a 34. 1. 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 t/ie other part, is equal to the square of the straight line which is made...
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