## The Elements of Euclid |

### From inside the book

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Page 13

The

The

**whole**is greater than its part . Book I. X. Two straight lines cannot enclose a space IX . OF EUCLID . 13 POSTULATES. ... Page 17

Wherefore the

Wherefore the

**whole**triangle ABC shall coincide with the**whole**triangle DEF , and be equal to it ; and the other angles of the one shall coincide with the remaining angles of the other , and be equal to them , viz . the angle ABC to the ... Page 18

... to which the equal sides are opsposite ; viz . the angle ACF to the angleABG , and the angle AFC to the angle AGB : and because the

... to which the equal sides are opsposite ; viz . the angle ACF to the angleABG , and the angle AFC to the angle AGB : and because the

**whole**AF is equal D E ito the**wholé**AG , of which the parts AB , AC , are equal ; the Auto renainder ... Page 37

Again ; B С because AB is parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore the

Again ; B С because AB is parallel to CE , and BD falls upon them , the exterior angle ECD is equal to the interior and opposite angle ABC ; but the angle ACE was shown to be equal to the angle BAC ; therefore the

**whole**exterior angle ... Page 39

... and the angle CBD to the angle ACB , the

... and the angle CBD to the angle ACB , the

**whole**angle ABD is equal to the**whole**angle ACD : and the angle BAC has been shown to be equal to the angle BDC ; therefore the opposite sides and apgles of parallelograms are equal to one ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

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