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

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Page 7

... BC is equal * 10 BG ; and because D is the centre of the circle GKI . , DL is equal to DG ; and + DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder * BG : but it has been

... BC is equal * 10 BG ; and because D is the centre of the circle GKI . , DL is equal to DG ; and + DA , DB , parts of them , are equal ; therefore the remainder AL is equal to the remainder * BG : but it has been

**shewn**, * 15 Def . Page 19

AB : neither is it less ; because then the angle ABC would be less than the angle ACB ; but it is not ; therefore the side AC is not less than AB : and it has been

AB : neither is it less ; because then the angle ABC would be less than the angle ACB ; but it is not ; therefore the side AC is not less than AB : and it has been

**shewn**that it is not equal to AB : therefore AC is greater than AB . Page 20

Again , because the two sides , CE , ED of the triangle CED are greater + than CD , add DB to each of these ; therefore the sides CE , EB , are greatert than CD , DB : but it has been

Again , because the two sides , CE , ED of the triangle CED are greater + than CD , add DB to each of these ; therefore the sides CE , EB , are greatert than CD , DB : but it has been

**shewn**that BA , AC are greater than BE , EC ; much ... Page 23

F + Hyp . not less than the angle EDF : and it was

F + Hyp . not less than the angle EDF : and it was

**shewn**that it is not equal to it ; therefore the angle BAC is greater than the angle EDF . Wherefore , if two triangles , & c . Q. E. D. B PROP . XXVI . THEOR . Page 27

Again , because the straight line GK cuts the parallel straight lines EF , CD , the angle E GHF is equal * to the angle GKD : and it was

Again , because the straight line GK cuts the parallel straight lines EF , CD , the angle E GHF is equal * to the angle GKD : and it was

**shewn**that the angle AGK is equal to the angle GHF ; therefore also AGK is equalt to GKD : and they ...### 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