## 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

... and because the tinition . point B is the centre of the circle ACE , BC is equal to BA : But it has been

... and because the tinition . point B is the centre of the circle ACE , BC is equal to BA : But it has been

**proved**that CA is equal to AB ; therefore CA , CB , are each of them equal to AB ; but things which are equal * 1st Ax- to the ... Page 10

... wherefore also the point C shall coincide with the point F , because the + Hyp . straight line AC + is equal to DF : but the point B was

... wherefore also the point C shall coincide with the point F , because the + Hyp . straight line AC + is equal to DF : but the point B was

**proved**to coincide with the point E ; wherefore the base BC shall coincide with the base EF ... Page 12

1 . angle ABG , and the angle AFC to the angle AGB : and because the whole AF is equal to the whole AG , of which the parts AB , AC , are * 3 Ax . equal ; the remainder BF is equal * to the remainder CG ; and FC was

1 . angle ABG , and the angle AFC to the angle AGB : and because the whole AF is equal to the whole AG , of which the parts AB , AC , are * 3 Ax . equal ; the remainder BF is equal * to the remainder CG ; and FC was

**proved**to be equal ... Page 14

Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been

Again , because CB is Hyp . equalt to DB , the angle BDC is equal * to the angle BCD ; but BDC has been

**proved**to be greater than the same BCD : which is impossible . The case in which the vertex of one triangle is upon a side of the ... Page 27

... and that the greater * angle is subtended by the * 19.1 . greater side , therefore the side EG is greater than the side EF : but EG was

... and that the greater * angle is subtended by the * 19.1 . greater side , therefore the side EG is greater than the side EF : but EG was

**proved**to be equal to BC ; therefore BC is greater than EF . Therefore if two triangles , & c .### 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