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

### From inside the book

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Page 2

... When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other is called a

... When a straight line standing on another straight line makes the adjacent angles equal to one another , each of the angles is called a right angle ; and the straight line which stands on the other is called a

**perpendicular**to it . Page 17

To draw a straight line

To draw a straight line

**perpendicular**to a given straight line of an unlimited length , from a given point without it . Let AB bé the given straight line , which may be produced to any length both ways , and let C be a point withс out ... Page 18

The straight line CH , drawn from the given point C , shall be

The straight line CH , drawn from the given point C , shall be

**perpendicular**to the given straight line AB . + Const , Join CF , CG : and because FH is equal to HG , and HC common to the two triangles FHC , GHC , the two sides FH ... Page 62

In obtuse angled triangles , if a

In obtuse angled triangles , if a

**perpendicular**be drawn from either of the acute angles to the opposite side produced , the square of the side subtending the obtuse angle , is greater than the squares of the sides containing the obtuse ... Page 63

the obtuse angle ACB , and from the point A let AD be drawn *

the obtuse angle ACB , and from the point A let AD be drawn *

**perpendicular**to BC produced : * 12 . 1 . the square of AB shall be greater than the squares of AC , CB , by tvrice the rectangle BC , CD . Because the straight line BD is ...### 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