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

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Page 3

An acute angle is that which is

An acute angle is that which is

**less**than a right angle . XIII , “ A term or boundary is the extremity of any thing . " XIV . A figure is that which is inclosed by one or more boundaries . XV . A circle is a plane figure contained by ... Page 7

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

If a straight line meets 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 that side ... Page 9

It is required to cut off from AB , the A E B greater , a part equal to C , the

It is required to cut off from AB , the A E B greater , a part equal to C , the

**less**. F From the point A draw * the straight line AD equal to C ; and from the centre A , and at the distance AD , describe * the * 3 Post . circle DEF ... Page 11

... cut off AG equal * to AF the

... cut off AG equal * to AF the

**less**, and * 3 . 1 . join FC , GB . Because AF is equal to + AG , and AB tofAC , Const . the two sides FA , AC are equal to the two GA , 6 Hyp . AB , each to each ; and they contain the angle FAG common ... Page 13

... and the triangle DBC is equal to the triangle * ACB , the

... and the triangle DBC is equal to the triangle * ACB , the

**less**to the D greater , which is absurd . Therefore AB is not unequal to AC , that is , it is equal to it . Wherefore , if two angles , & c . Q. E. D. B * * 4.1 . с - Cor .### 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