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" If a straight line be divided into any two parts, the square of the whole line is equal to the squares of the two parts, together with twice the rectangle contained by the parts. "
The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... - الصفحة 41
بواسطة Euclides - 1816 - عدد الصفحات: 528
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The first six books of the Elements of Euclid, with numerous exercises

Euclides - 1853 - عدد الصفحات: 147
...lines ab, ас is sometimes simply called the rectangle ab, ac. Я PROPOSITION IV. — THEOREM. If a straight line be divided into any two parts, the square of the whole line is equal to the squares oftíie two parts, togetlwr with twice the rectangle contained by the parts. LET the straight line...
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The Elements of Euclid, books i-vi; xi. 1-21; xii. 1,2; ed. by H.J. Hose

Euclides - 1853
...THEOE. If a straight line be divided into any two parts: then the square of the whole line shall be equal to the squares of the two parts together with twice the rectangle contained by the two parts. Let the straight line AB be divided into any two parts AC, CB in c. Then the square of AB...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

Royal Military Academy, Woolwich, Thomas Stephens Davies, Stephen Fenwick, William Rutherford - 1853
...rectangles contained by the whole and each of the parts are together equal to the square of the whole line. Let the straight line AB be divided into any two parts in the point C ; the rectangle contained by AB, BC, together with the rectangle* AB, AC, shall be equal...
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The Elements of Euclid: With Many Additional Propositions ..., الجزء 1

Euclid - 1853 - عدد الصفحات: 136
...then (a) I. 46. (6 VI. 31. (c) Constr. (/) I. 34. a'2 = am -f- a n. PROPOSITION III. THEOREM. — If a straight line (AB) be divided into any two parts (in C), the rectangle under the whole line (AB) and one of those parts (CB) is equal in area to the square on that...
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Report of twenty-one years' experience of the Dick bequest for elevating the ...

Allan Menzies - 1854
...Euclid's general reasoning, and point out the part of your demonstration in which it is evaded. 3. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. A modification of what you have here proved constitutes the rule for the extraction of the square root....
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Annual Report of the Normal, Model, and Common Schools in Upper Canada for ...

Upper Canada. Chief Superintendent of Schools - 1854
...required in the demonstrations of the 7th, 27th, 32nd and 48th prop, of the 1st book of Euclid. . 3. If a straight line be divided into any two parts, the...the squares of the two parts, together with twice their rectangle. 4. If a straight line be divided into two equal and also into two unequal parts ;...
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Elements of geometry and mensuration

Thomas Lund - 1854 - عدد الصفحات: 362
...each, to which the equal sides are opposite, .-. / ACS = / BCD = a right angle. 44. PROP. XXII. If a straight line be divided into any two parts, the square of the whole line is equal to the sum of the squares of the two parts together with twice the rectangle* contained by the parts. QDEF....
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Skeleton propositions &c. of Euclid, books i and ii, with ..., المجلد 2

Euclides - 1858
...I, Ax. 1. Hyp. Cone. •ui Con e. Def. 1.1 1. .in. I. \x. I. BOOK II. 85 PROP. IV. THEOII. If a st. line be divided into any two parts, the square of the whole line equals the squares of the two parts, together with twice the rectangle contained by the parts. CоN....
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Examination papers used at the examinations for admission to the Royal ...

Sandhurst roy. military coll - 1859 - عدد الصفحات: 1869
...the following equations ,-, 2x + 5 5 2x-5 3 2.a? + 7 2j;-7 __ 1^ ~ 14 21 1 (2) bx-ay=d EUCLID. 1. If a straight line be divided into any two parts, the...together with twice the rectangle contained by the parts. 2. In every acute-angled triangle the square of the side subtending either of the acute angles is less...
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A test-book for students; comprising sets of examination papers upon ...

Thomas Stantial - 1859
...the features of "parallel lines" and "parallelograms" gained from the first book of Euclid. 3. " If a straight line be divided into any two parts, the square of the whole line is equal to the rectangles contained by the whole and each part." Prove this (1) by geometry ; (2) by algebraic demonstration...
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