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" PROP. VIII. THEOR. IF a straight line be divided into any two parts, tour 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 Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ... - Seite 59
von Robert Simson - 1806 - 518 Seiten
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Gradations in Euclid : books i. and ii., with an explanatory preface [&c ...

Euclides - 1858 - 248 Seiten
...the figures ; hence the use of k. PROP. 3. — THEOR. If a st. line be divided into any two parts, the rectangle contained by the whole line and one of the parts, is equal to the rectangle contained by the two parts together with the square of the aforesaid part....
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Euclid's Elements of plane geometry [book 1-6] explicitly enunciated, by J ...

Euclides - 1860 - 288 Seiten
...rectangle AB • BC. PROPOSmON VIII. THEOREM. 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 on the other part, is equal to the square on the straight line which is made up of the whole and the...
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Government examinations, a companion to 'Under government' and a key to the ...

Joseph Charles Parkinson - 1860 - 154 Seiten
...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 up of the half and the part produced. 8. PROP. XII. — In obtuse-angled triangles, if a perpendicular be drawn...
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A complete practical guide to her majesty's Civil service, by a certificated ...

Civil service - 366 Seiten
...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 up of the half and the part produced. PEOP. XII. — In obtuse-angled triangles, if a perpendicular be drawn...
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Guide to the Three Services: Civil, Naval, and Military

John Paxton Hall - 1860 - 186 Seiten
...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 up of the half and the part produced. PROP. XII. — In obtuse-angled triangles, if a perpendicular be drawn...
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Euclid's Elements of Geometry: Chiefly from the Text of Dr. Simson, with ...

Robert Potts - 1860 - 380 Seiten
...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, Teil 1

James Elliot - 1860 - 252 Seiten
...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. £a ( V 5 —...
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The examination papers as set for the preliminary literary examination of ...

Royal college of surgeons of England - 1860 - 336 Seiten
...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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The elements of algebra. [With] Answers

Robert Fowler - 1861 - 426 Seiten
...&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 Seiten
...straight line, &o. QED PROPOSITION 8. -THEOREM. 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 on the other part, is equal to the square on the straight line which is made up of the whole line and...
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