## The Elements of Euclid |

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Page 13

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 43

IF a parallelogram and triangle be uport the same base , and between the same parallels ; the parallel - gram shall be

IF a parallelogram and triangle be uport the same base , and between the same parallels ; the parallel - gram shall be

**double**of the triangle . Book I. Let the parallelogram ABCD and the triangle EBC OF EUCLID . Page 44

Book I. Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE , the parallelogram ABCD is

Book I. Let the parallelogram ABCD and the triangle EBC be upon the same base BC , and between the same parallels BC , AE , the parallelogram ABCD is

**double**of the triangle EBC . A D E Join AC ; then the triangle ABC i 37. Page 49

But the

But the

**doubles**of equals are equal k to one another : h 6. AE . therefore the parallelogram BL is equal to the square GB : and in the same manner , by joining AE , BK , it is demonstrated that the parallelogram CL is equal to the ... Page 57

1 . therefore equal to the whole CE ; therefore AK , CE are

1 . therefore equal to the whole CE ; therefore AK , CE are

**double**of A с B AK : but AK , CE are the gnomon • AKF together with the squale CK ; therefore the gnomon AKF , togeG ther with the square CK , is**double**H н K of AK : but twice ...### What people are saying - Write a review

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### Other editions - View all

The Elements of Euclid: The Errors, by Which Theon, Or Others, Have Long Ago ... Robert Simson,Robert Euclid No preview available - 2015 |

The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh ... Robert Simson,Robert Euclid No preview available - 2016 |

### Common terms and phrases

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