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" If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line. "
The examination papers as set for the preliminary literary examination of ... - Σελίδα 1
των Royal college of surgeons of England - 1860
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The English Journal of Education, Τόμος 2

1848
...Tate's Geometry," &c. page 39, where a new proof is given of this important theorem. SECTION 3. 1. If a straight line be divided into two equal parts,...parts, the rectangle contained by the unequal parts, togelher with the square of the line between the points of section, is equal to the square of half...

The first three books of Euclid's Elements of geometry, with theorems and ...

Euclid, Thomas Tate - 1849 - 108 σελίδες
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOR. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point c, and into two unequal parts...

The Calendar of King's College, London

1850
...produced, the exterior angle is greater than either of the interior opposite angles. 2. If a right line be divided into two equal parts, and also into...section, is equal to the square of half the line. 3. In every triangle, the square of the side subtending either of the acute angles, is less than the...

A Collection of Problems and Examples Adapted to the "Elementary Course of ...

Harvey Goodwin - 1851 - 173 σελίδες
...divided into four equal parts. In what case will the diameter bisect the angle of a parallelogram? 3. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. 4. Equal straight lines in a circle are equally distant from the centre ; and conversely, those which...

The English Journal of Education, Τόμος 5

1851
...a given rectilineal angle. upon the same side together equal to two right angles. SECTION II.—1. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. 3. The opposite angles of any quadrilateral figure inscribed in a circle are together equal to two...

The First Two Books of the Elements of Euclid ... with Additional Figures ...

Euclides - 1852
...same may be shown of any other division of 8, as into 6 and 2, or 7 and 1.] BOOK II. PROP. V. THEOR. If a straight line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...

A Practical Treatise on Algebra: Designed for the Use of Students in High ...

Benjamin Greenleaf - 1852 - 336 σελίδες
...c=3. Then 12=9+3; And 4Xl2X9+3 2 =(3X2X9) 2 ; 441 = 441. THEOREM XIII. 17O. If any quantity or number be divided into two equal parts, and also into two unequal parts, the sum of the squares of the two unequal parts will be double the squares of half the quantity, plus twice...

The synoptical Euclid; being the first four books of Euclid's Elements of ...

Euclides - 1853
...manifest that the parallelograms about the diameter of a square are likewise squares. PROP. V. THEOREM. If a straight 'line be divided into two equal parts,...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...

The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - 147 σελίδες
...the parallelograms about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts,...points of section, is equal to the square of half the Une. LET the straight line ab be divided into two equal parts in the point С, and into two unequal...

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

Euclid, John Playfair - 1853 - 317 σελίδες
...line is divided be denoted by a and b; then, (a+6)* PROP. V. THEOR. If a straight line bcdividedinto two equal parts, and also into two unequal parts;...section, is equal to the square of half the line. Let the straight line AB be divided into two equal parts in the point C, and into two unequal parts...




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