| Euclides - 1853 - 176 Seiten
...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... | |
| Euclides - 1853 - 334 Seiten
...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... | |
| Royal Military Academy, Woolwich - 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... | |
| Euclid - 1853 - 176 Seiten
...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... | |
| Allan Menzies - 1854 - 520 Seiten
...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.... | |
| Upper Canada. Chief Superintendent of Schools - 1854 - 192 Seiten
...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 ;... | |
| Thomas Lund - 1854 - 518 Seiten
...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.... | |
| Euclides - 1858 - 134 Seiten
...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.... | |
| Sandhurst roy. military coll - 1859 - 672 Seiten
...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... | |
| Thomas Stantial - 1859 - 352 Seiten
...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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