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

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Page 7

To describe an equilateral triangle upon a given finite straight line . Let AB be the

To describe an equilateral triangle upon a given finite straight line . Let AB be the

**given straight line**; it is required to describe an equilateral triangle upon AB . From the centre A , at the distance AB , describe * the circle BCD ... Page 8

Wherefore from the given point A a straight line AL has been ' drawn equal to the

Wherefore from the given point A a straight line AL has been ' drawn equal to the

**given straight line**BC . Which was to be done . PROP . III . PROB . ... From the greater of two**given straight lines**to cut off a part equal to the less . Page 13

1 . teral triangle DEF ; then join AF : the

1 . teral triangle DEF ; then join AF : the

**straight line**AF shall bisect the angle BAC . Because AD is equal + to AE ... To bisect a**given**finite**straight line**, that is , to divide it into two equal parts . Let AB be the**given**... Page 14

The straight line FC drawn from the given point C , shall be at right angles to the

The straight line FC drawn from the given point C , shall be at right angles to the

**given straight line**AB . Because DC is equal t to CE , and FC common to the two triangles DCF , ECF ; the two sides DC , CF , are equal to the two EC ... Page 15

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

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

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

added altitude angle ABC angle BAC base Book centre circle circle ABCD circumference common cone contained cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular equimultiples Euclid excess figure fore four fourth given angle given in position given in species given magnitude given ratio given straight line greater Greek half join less likewise logarithm magnitude manner meet multiple opposite parallel parallelogram pass perpendicular plane prism produced PROP proportionals proposition proved pyramid radius reason rectangle rectilineal figure remaining right angles segment shewn sides similar sine solid sphere square square of AC taken THEOR third triangle ABC wherefore whole