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" If a straight line be bisected, and produced to any point; the rectangle contained by the whole line thus produced, and the part of it produced, together with the square of half the line bisected, is equal to the square of the straight line which is made... "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 83
by Euclides - 1871
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The first two books of the Elements of Euclid, with additional figures ...

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...
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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
...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...
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The Elements of Euclid: With Many Additional Propositions ..., Part 1

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....
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The synoptical Euclid; being the first four books of Euclid's Elements of ...

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...
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The first six books of the Elements of Euclid, with numerous exercises

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...
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The geometry, by T. S. Davies. Conic sections, by Stephen Fenwick

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...
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Solutions of the problems and riders proposed in the Senate-house ...

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...
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Solutions of the Problems and Riders Proposed in the Senate-house ...

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...
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The Elements of geometry; or, The first six books, with the eleventh and ...

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...
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Elements of Geometry: Containing the First Six Books of Euclid with a ...

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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