## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth |

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Page 280

... a definition was as necessary and useful s to be

... a definition was as necessary and useful s to be

**given**in that book as in this : but indeed there “ is scaree any ... as this was the proper place for it ; duplicate and triplicate ratio being**species**of compound ratio : but Theon ... Page 337

Rectilineal figures are said to be

Rectilineal figures are said to be

**given in species**, which have each of their angles given , and the ratios of their sides given . IV . Points , lines , and spaces , are said to be given in posiare either actually exhibited , or can be ... Page 366

A in position , be cut by the straight line GHK ; the ratio of GH to HK is given . In AB take a given point L , and draw LM perpendicular ... If each of the sides of a triangle be given in magnitude ; the triangle is

A in position , be cut by the straight line GHK ; the ratio of GH to HK is given . In AB take a given point L , and draw LM perpendicular ... If each of the sides of a triangle be given in magnitude ; the triangle is

**given in species**. Page 367

Á Take a straight line DE given in position and magnitude , and at the points D , E , make * the angle EDF equal D * 23 . 1 . to the angle BAC , and the angle ... ABC ; which therefore is

Á Take a straight line DE given in position and magnitude , and at the points D , E , make * the angle EDF equal D * 23 . 1 . to the angle BAC , and the angle ... ABC ; which therefore is

**given in species**. * 4.6 . 1 Def . 6 . PROP . Page 368

42 Dat . wherefore DE , EF , FD are

42 Dat . wherefore DE , EF , FD are

**given*** in magnitude ; and the triangle DEF is therefore**given*** in**species**; and because the triangles ABC , DEF have one angle BAC equal to one angle EDF , and the sides about these angles ...### What people are saying - Write a review

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The Elements of Euclid: Viz. The First Six Books, Together With the Eleventh ... Euclid Euclid No preview available - 2018 |

### Common terms and phrases

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole