| Euclides - 1852 - 152 pages
...line between the points of section (16), added together, ie double of 52.] B 4 BOOK n. PROP. X. THEOR. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Euclides - Geometry - 1853 - 334 pages
...was to be proved. PEOP. VI. THEOE. If a straight line be bisected, and produced to any point : then **the rectangle contained by the whole line thus produced...the part of it produced, together with the square** of half the bisected line, shall be equal to the square of the line, which is made up of the half and... | |
| Euclid - Geometry - 1853 - 176 pages
...and the produced part, to• gether with the square on <• half the line bisected, is equal in area **to the square on the straight line which is made up of the half and the** produced part. 11.10.. . II. 11, cor. II. 4, cor. 2.. . II. 1. . II. l.cor. II. 5, schol. 2. . II.... | |
| Euclides - 1853 - 146 pages
...DB, are double of the squares of AC, CD. Therefore, if a straight line, &c. Q ED PROP. X. THEOREM. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Euclides - 1853 - 176 pages
...double of the squares of a С, С d. If therefore a straight line, &c. QED PBO POSITION X. — THEOREM. **If a straight line be bisected, and produced to any point, the** square of the whole luie thus produced, and the square of the part of it produced, are together double... | |
| Royal Military Academy, Woolwich - Mathematics - 1853 - 400 pages
...DB are double of the squares of AC, CD. If therefore a straight line, etc. QED PROPOSITION X. THEOR. **If a straight line be bisected, and produced to any point, the** square of the whole line thus produced, and the square of the part of it produced, are together double... | |
| Cambridge univ, exam. papers - 1854 - 282 pages
...shall be equal to the square of the other part. Produce a given straight line to a point such that **the rectangle contained by the whole line thus produced and the part** produced shall be equal to the square of the given straight line. In Euclid's figure, the rectangle... | |
| William Walton, Charles Frederick Mackenzie - Mathematics - 1854 - 266 pages
...shall be equal to the square of the other part. Produce a given straight line to a point such that **the rectangle contained by the whole line thus produced and the part** produced shall be equal to the square of the given straight line. In Euclid's figure, the rectangle... | |
| Euclides - 1855 - 262 pages
...contained by the sum and the difference of the hypotenuse and the other leg. PEOP. VI. THEOBEM ya ttraight **line be bisected, and produced to any point, the rectangle...the part of it produced, together with the square** of half the line bisected, is equal to the square of the straight Kne which is made up of the half... | |
| John Playfair - Geometry - 1855 - 336 pages
...contain" ed by their sum and difference, or that AC 2 — CD 2 =(AC+CD) (AC — SCHOLIUM. PROP. VI THEOR. **If a straight line be bisected, and produced to any point; the rectangle** contamed by the whole line thus produced, and the part of it produced, together with the square of... | |
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