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

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Page 71

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 cuts it at right angles it shall bisect it . Page 72

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 euch other . Let ABCD be a circle , and AC , BD two straight lines in it which cut one another in the point E , and do ... Page 78

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 contaci . Let the two circles ABC , ADE touch each 1 . * 9.3 . DGE S 1 . other internally in the ... Page 79

DGE S 1 . other internally in the point A ; and let F be the centre of the circle ABC , and G the centre of the circle ADE ; the straight line which joins the centres F , G , being produced , shall

DGE S 1 . other internally in the point A ; and let F be the centre of the circle ABC , and G the centre of the circle ADE ; the straight line which joins the centres F , G , being produced , shall

**pass**HA through the point A. For ... Page 80

AG : but it is also * less ; which is impossible : therefore the straight line which joins the points F , G , cannot

AG : but it is also * less ; which is impossible : therefore the straight line which joins the points F , G , cannot

**pass**otherwise than through the point of contact A , that is , it must**pass**through it . Therefore , if two circles ...### 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

altitude angle ABC angle BAC base base BC BC is equal centre circle ABCD circumference common cone Const contained cylinder demonstrated described diameter divided double draw drawn equal angles equiangular equilateral equimultiples extremities fall figure fore four fourth given given straight line greater half inscribed join less Let ABC likewise magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism PROB produced PROP proportionals proved pyramid ratio reason rectangle contained rectilineal figure remaining angle right angles segment shown sides similar solid solid angle solid parallelopiped sphere square taken THEOR third touches triangle ABC vertex wherefore whole