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

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Page 57

If a straight line drawn through the centre of a circle bisect a straight line in it which does not

If a straight line drawn through the centre of a circle bisect a straight line in it which does not

**pass**through the centre , it shall cut it at right angles : and if it cut it at right angles , it shall bisect it . Page 58

If in a circle two straight lines cut one another , which do not both

If in a circle two straight lines cut one another , which do not both

**pass**through the centre , they do not bisect each other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the ... Page 63

If two circles touch each other internally , the straight line which joins their centres being produced shall

If two circles touch each other internally , the straight line which joins their centres being produced shall

**pass**through the point of contact . Let the two circles ABC , ADE touch each other internally in the point A ; and let F be ... Page 64

Therefore the straight line which joins the points F , G , being produced , cannot fall otherwise than upon the point X , that is , it must

Therefore the straight line which joins the points F , G , being produced , cannot fall otherwise than upon the point X , that is , it must

**pass**through it . Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . Page 65

3 . through the point of contact : but it does not

3 . through the point of contact : but it does not

**pass**through it , because the points B , D , are without the straight line GH ; which is absurd : therefore one circle cannot touch another on the inside in more points than one .### 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