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" If a straight line be divided into any two parts, four times the rectangle contained by the whole line, and one of the parts, together with the square of the other part, is equal to the square of the straight line which is made up of the whole and that... "
Elements of geometry, containing the first two (third and fourth) books of ... - Page 86
by Euclides - 1871
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 pages
...in the point C ; to prove that four times the rectangle AB • BC, together with the square on AC, is equal to the square on the straight line, which is made up of AB and BC together. (Const.) Produce AB to D, so that BD be equal to CB, and upon AD describe the square...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860 - 332 pages
...made up of the half and the part produced. 8. Divide a given straight line into two parts, such that the rectangle contained by the whole line and one of the parts may be equal to the square of the other part. PRELIMINARY GENERAL EXAMINATION. Christmas, 1864. WEDNESDAY,...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - Geometry, Plane - 1860 - 380 pages
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. FG it Upon AB describe the square A CDB ; (l. 46.)...
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An elementary course of practical mathematics, Part 1

James Elliot - 1860 - 252 pages
...Ex. C), the altitude of the triangle being a and the base b 1 8. A st* line a being divided so that the rectangle contained by the whole line and one of the parts is equal to the square of the other part, compute the lengths of the two parts. Ans. Ła ( V 5 —...
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Examination papers used at the examination of candidates for appointment to ...

War office - 1861 - 260 pages
...line thus produced and the part of it produced, together •with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced. 3. In a circle the angle in a semicircle is a right angle, but the angle...
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The elements of algebra. [With] Answers

Robert Fowler - 1861 - 426 pages
...&c. &c. according to the explanations in p. 7. 5. Divide a line а feet long into two parts, so that the rectangle contained by the whole line and one of the parts shall be equal to the square of the other part. Let x = the length of the greater part, in feet. ....
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Euclid's Elements of geometry, books i. ii. iii. iv

Euclides - 1862 - 140 pages
...line thus produced, ana, the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced. (References — Prop. I. 31, 34, 36, '43, 46; II. 4, cor.) Hypothesis....
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Responsions

University of Oxford - Education, Higher - 1863 - 316 pages
...line thus produced, and the part of it produced, together with the square on half the line bisected, is equal to the square on the straight line which is made up of the half and the part produced. 10. If a straight line be divided into two equal, and also into two unequal...
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The elements of plane geometry; or, The first six books of Euclid, ed. by W ...

Euclides - 1863 - 122 pages
...straight line (AB) be divided into ang two parts (at C), Jour times the rectangle (AB, BC) contained bg the whole line, and one of the parts, together with the square of the other part (AC), is equal to the square of the straigh t line (AD), which is made up of the...
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The school edition. Euclid's Elements of geometry, the first six books, by R ...

Euclides - 1864 - 448 pages
...other part. Let AB be the given straight line. It is required to divide AB into two parts, so that the rectangle contained by the whole line and one of the parts, shall be equal to the square on the other part. c KD Upon AB describe the square A CSB; (i. 46.) bisect...
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