## The Elements of Euclid |

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Page 14

“ If a straight line meet two straight lines , so as to make the “ two interior angles on the same side of it taken together

“ If a straight line meet two straight lines , so as to make the “ two interior angles on the same side of it taken together

**less**" than two right angles , these straight lines being continually “ produced , shall at length meet upon ... Page 16

PROB . t + FROM the greater of two given straight lines to cut off a part equal to 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

1 . equal to AC , the

1 . equal to AC , the

**less**, and join DC ; thereА fore , because in the triangles DBC , ACB , DB is equal to AC , and BC common to D both , the two sides DB , BC are equal to the two AC , CB , each to each ; and the angle DBC is equal ... Page 26

ANY two angles of a triangle are together

ANY two angles of a triangle are together

**less**than two right angles . Let ABC be any triangle ; any А two of its angles together are**less**than two right angles . Produce BC to D ; and be . cause ACD is the exterior anyle of the ... Page 27

In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are

In like manner , it may be demonstrated , that BAC , ACB , as also CAB , ABC , are

**less**than two right angles , Therefore any two angles , & c . Q. E. D. 2.9 PROP . XVIII , THEOR . U THE greater side of every triangle is opposite to the ...### 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