 | Euclides - Geometry - 1853 - 176 pages
...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 - Geometry - 1853 - 334 pages
...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 - Mathematics - 1853 - 400 pages
...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 - Geometry - 1853 - 176 pages
...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 pages
...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 - Education - 1854 - 196 pages
...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 - Geometry - 1854 - 520 pages
...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 - 136 pages
...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 pages
...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 - Examinations - 1859 - 352 pages
...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... | |
| |
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. 
