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

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Page 6

... 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 , 6 EUCLID'S ELEMENTS . AXIOMS. Page 7

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 . Tag es which coincide with one another , that is , which exactly fill the same space ... Page 37

... the parallelograms ABCD , DBCF , opposite to the base BC , he terminated in the same point D ; it is plain that each of the paral- B lelograms is

... the parallelograms ABCD , DBCF , opposite to the base BC , he terminated in the same point D ; it is plain that each of the paral- B lelograms is

**double*** of the triangle BDC ; and they are therefore equal t to +6 Ax . one another . Page 41

1 . parts ; wherefore ABCD is also

1 . parts ; wherefore ABCD is also

**double**of the triangle EBC . Therefore , if a parallelogram , & c . Q. E. D. * 37 . 1 . : ; PROP . XLII . PROB . To describe a parallelogram that shall be equal to a given triangle , and have one of ... Page 42

1. the parallelogram FECG is likewise

1. the parallelogram FECG is likewise

**double*** of the triangle AEC , because they are upon the same base EC , and between the same parallels EC , AG : therefore the parallelogram FECG is +6 Ax . equalt to the triangle ABC ; and it has ...### 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