## The Elements of Euclid |

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Page 16

PROB . t + FROM the

PROB . t + 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 , the**greater**, a part equal to C ... Page 19

Let ABC be a triangle having the angle ABC equal to the Book L angle ACB ; the side AB is also equal to the side Ac . For if AB be not equal to AC , one of them is

Let ABC be a triangle having the angle ABC equal to the Book L angle ACB ; the side AB is also equal to the side Ac . For if AB be not equal to AC , one of them is

**greater**than the other : let AB be the**greater**, and from it cut off DB ... Page 20

1 . equal to one another , but the angle ECD is

1 . equal to one another , but the angle ECD is

**greater**than the angle BCD ; wherefore the angle FDC is likewise**greater**than BCD ; much more than is the angle BDC**greater**then the angle BCD . Again , because CB is equal to DB ... Page 26

IF one side of a triangle be produced , the exterior angle is

IF one side of a triangle be produced , the exterior angle is

**greater**than either of the interior opposite angles . a 10. 1 . Y D b 15. 1 . Let ABC be a triangle , and let its side BC be produced to D , the exterior angle ACD is**greater**... Page 27

1 these add the angle ACB ; therefore the angles ACD , ACB Book I. are

1 these add the angle ACB ; therefore the angles ACD , ACB Book I. are

**greater**than the angles ABC , ACB ; but ACD , ACB are together equal b to owo right angles ; therefore the angles b 13. 1 . ABC , BCA are less than two right angles ...### 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