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

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Page 67

A straight line is said to

A straight line is said to

**touch**a circle , when it meets the circle , and being produced does not cut it . O III . Circles are said to**touch**one another , which meet , but do not cut one another , IV . Straight lines are said to be ... Page 73

Therefore E is not the centre of the circles ABC , CDG . Wherefore , if two circles , & c . Q.E.D. † 15 Def , 1 . t1 Ax . PROP . VI . THEOR . If two circles

Therefore E is not the centre of the circles ABC , CDG . Wherefore , if two circles , & c . Q.E.D. † 15 Def , 1 . t1 Ax . PROP . VI . THEOR . If two circles

**touch**one another internally , they shall not have the same centre . Page 78

If two circles

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

If two circles

If two circles

**touch**each other externally , the straight line which joins their centres shall pass through the point of contact . Let the two circles ABC , ADE ,**touch**each other externally in the point A ; and let F be the centre of ... Page 80

One circle cannot

One circle cannot

**touch**another in more points than one , whether it**touches**it on the inside of outside . For , if it be possible , let the circle EBF**touch**the circle ABC in more points than one , and first on the inside , in the ...### 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