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

### From inside the book

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Page 5

... the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are

... the remainders are equal . IV . If equals be added to unequals , the wholes are unequal . V. If equals be taken from unequals , the remainders are unequal . VI . Things which are

**double**of the same , BOOK I. - DEFINITIONS , & c . 5. Page 6

Things which are

Things which are

**double**of the same , are equal to one another . VII . Things which are halves of the same , are equal to one another . VIII . Magnitudes which coincide with one another , that is , which exactly fill the same space ... Page 30

If the sides AD , DF of the parallelograms ABCD , DBCF , opposite to the base BC , be terminated in the same point D ; it is plain that each of the parallelograms is

If the sides AD , DF of the parallelograms ABCD , DBCF , opposite to the base BC , be terminated in the same point D ; it is plain that each of the parallelograms is

**double*** of the triangle BDC ; and they are therefore equal + to one ... Page 33

If a parallelogram and a triangle be upon the same base , and between the same parallels ; the parallelogram shall be

If a parallelogram and a triangle be upon the same base , and between the same parallels ; the parallelogram shall be

**double**of the triangle . * 37.1 . Let the parallelogram ABCD and the triangle BOOK I. PROP . XL , XLI . 39. Page 34

Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE : the parallelogram D E ABCD shall be

Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE : the parallelogram D E ABCD shall be

**double**of the triangle · EBC . Join AC : then the triangle ABC is equal * to the ...### 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