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" TO divide a given ftraight line into two parts, fo that the rectangle contained by the whale, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight line; it is required to divide it into two parts, fo that... "
A Complete Treatise on Practical Mathematics: Including the Nature and Use ... - Pagina 417
door John McGregor (teacher of mathematics.) - 1792 - 431 pagina’s
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The Elements of Euclid: The Errors, by which Theon, Or Others, Have Long Ago ...

Robert Simson - 1762 - 466 pagina’s
...PR OB. TO divide a given ftraight line into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight line ; it is required to divide it into two parts, fo that the rectangle...
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Euclid's Elements of Geometry: The First Six, the Eleventh and Twelfth Books

Euclid - 1765 - 464 pagina’s
...this, there being no number that can be divided into two others f«ch, that the product of the whole by one of the parts, fhall be equal to the fquare of the other part. PROP. XII. THE OR. In obtufe-axgicd triangles, the fquare of the fide eppofite to the obtufe angle,...
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The Elements of Euclid, Viz: The Errors, by which Theon, Or Others, Have ...

Robert Simson - 1775 - 520 pagina’s
...ftraight line ; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB deferibe * the fquare ABDC ; bifect b AC in E, and join BE ; produce CA to F, and makec EF...
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The First Six Books: Together with the Eleventh and Twelfth

Euclid - 1781 - 520 pagina’s
...PRO B. TO divide a given ftraight line into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given ftraight line ; it is required to divide it into two parts, fo that the rectangle...
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The Young Geometrician's Companion: Being A New and Comprehensive ..., Volume 6

Richard Turner - 1787 - 240 pagina’s
...Right Line given into extreme and meati Proportion ; that is, to cut a Line fo that the Product of the whole Line and one of the Parts fhall be equal to the Square of the other Part. Let AB be the Right Line given to be fo divided. 11 «L AC Cbnftruflion....
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

Euclid - 1789 - 272 pagina’s
...AB be the given right line ; it is required to divide it into two parts, fo that the reŁtangle of the whole line and one of the parts fhall be equal to the fquare of the other part. Upon AB defcribe the fquare AC (II. i.), and bifeft the fide of it AD in E (I. 10.) Join the points...
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Elements of Geometry;: Containing the First Six Books of Euclid, with Two ...

John Playfair - 1795 - 400 pagina’s
...the lines." PR O P. VIII. THEO R." TF a ftraight line be divided into any two parts, J. four times the reftangle contained by the whole line, and one of the parts, together with the fquare of the other part, is equal to the fquare of the ftraight line which is made...
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The Elements of Euclid: Viz. the First Six Books, with the Eleventh and ...

Alexander Ingram - 1799 - 351 pagina’s
...it is required to divide CoIK II. it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB defcribe » the fquare ABDC ; bifea b AC in E, and join BE ; produce CA to F, and make c EF...
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Elements of Geometry: Containing the Principal Propositions in the First Six ...

John Bonnycastle - 1803 - 279 pagina’s
...PROP. XXII. PROBLEM. • • - y To divide a given right line into two parts, fo that the re&angle contained by the whole line and one of the parts, fhall be equal to the fquare of the other part. Let AB be the given right line ; it is required to divide it into two parts, fo that the reftangle...
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The Elements of Euclid: Also the Book of Euclid's Data ...cor. viz. The ...

Robert Simson - 1804
...ftraight line; it is required to divide it into two parts, fo that the rectangle contained by the whole, and one of the parts, fhall be equal to the fquare of the other part. Upon AB defcribe » the fquare ABDC, bifect b AC in E, and join BE; produce CA to F, and make c EF...
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