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

### From inside the book

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Page 8

From the greater of two given straight lines to cut off a part equal to the

From the greater of two given straight lines to cut off a part equal to the

**less**. Let AB and C be the two given straight lines , whereof AB is the greater . It is required to cut off from AB , Е В the greater , a part equal to C ... Page 18

Let ABC be any triangle ; any two of its angles together shall be

Let ABC be any triangle ; any two of its angles together shall be

**less**than two right angles . Produce BC to D ; and because ACD is the exterior angle of the triangle ABC , ACD is greater * than the interior and opposite angle ABC ... Page 19

For , if it be not greater , AC must either be equal to AB , or

For , if it be not greater , AC must either be equal to AB , or

**less**than it : it is not equal , because then the angle ABC would be equal * to the angle CAB ; but it * 5. 1 . ist not ; therefore AC is not equal to + Hyp . Page 23

10 to EF : but it ist not : therefore + Hyp . the angle BAC is not equal to the angle EDF : neither is it

10 to EF : but it ist not : therefore + Hyp . the angle BAC is not equal to the angle EDF : neither is it

**less**, because then the base BC would be**less**than the base EF ; but it is + ... Page 26

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**less**than two right angles : but those straight lines which , with another straight line falling upon them , make the interior angles on the same side**less**than two right angles , will meet * together if continually produced ...### 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