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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 on the line between the points of section, is equal to the square on half the line. "
The Elements of Euclid; viz. the first six books,together with the eleventh ... - Page 53
by Euclides - 1841 - 351 pages
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The English Journal of Education, Volume 5

Education - 1851 - 502 pages
...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, and also into two...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...
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A Practical Treatise on Algebra: Designed for the Use of Students in High ...

Benjamin Greenleaf - Algebra - 1852 - 348 pages
...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...
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - Geometry - 1853 - 178 pages
...about the diameter of a square are likewise squares. PROPOSITION V. — THEOREM. If a straight line be divided into two equal parts, and also into two...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...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose, Book 1

Euclides - Geometry - 1853 - 334 pages
...proved. PEOP. V. THEOE. If a straight line be bisected, and also divided into two unequal parts : then the rectangle contained by the unequal parts together with the square of the part of the line intercepted between the points of section, shall be equal to the square of half the...
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Orr's Circle of the Sciences: Organic nature, vols. 1-3 (1854-1856)

William Somerville Orr - Science - 1854 - 534 pages
...л straight line (AB) be divided into two equal parts (inC), and also info two unequal parts (in D), the rectangle contained by the unequal parts, together with the square of (CD), the line between the points of section, is equal to the square of hilf the line : that is, DB...
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The Elements of geometry; or, The first six books, with the eleventh and ...

Euclides - 1855 - 262 pages
...into turn equal parts, and also into two unequal part'; the rectangle contained by the unequal parta, together with the square of the line between the points of section (or division), is equal to the square of half the line. Let the straight line AB be divided into two...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 252 pages
...its angles equal to a given rectilineal angle. Is this a determinate problem? 6. If a straight line be divided into two equal parts, and also into two...section, is equal to the square of half the line. Prove this proposition algebraically. 6. Find the centre of a given circle. Shew that if in a circle...
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The geometry of the three first books of Euclid, by direct proof from ...

Euclides - 1856 - 168 pages
...of a square are likewise squares. L. — EUCLID II. 5. If a straight line be divided into two equal and also into two unequal parts, the rectangle contained...square of half the line. Let the straight line AB (Fig. 40) be divided into two equal parts at the point C, and into two unequal parts at the point D;...
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Cambridge examination papers: a suppl. to the University calendar, 1856-59

Cambridge univ, exam. papers - 1856 - 200 pages
...times that on one of the sides; compare the two sides. 4. If a straight line be divided into two equal and also into two unequal parts; the rectangle contained...of section is equal to the square of half the line. State this result algebraically. 5. Draw a straight line from a given point, either without or in the...
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National Society's Monthly Paper

1857 - 408 pages
...other two sides of it, the angle contained by these two sides is a right angle. 5. If a straight line be divided into two equal parts, and also into two unequal parts, the reptangle contained by the unequal parts, together with the square of the line between the points of...
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