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

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Page 102

Magnitudes which have the same ratio are called

Magnitudes which have the same ratio are called

**proportionals**. • N.B. When four magnitudes are**proportionals**, it is usually expressed by saying , the • first is to the second , as the third to the fourth . ' VII . Page 103

In

In

**proportionals**, the antecedent terms are called homologous to one another , as also the consequents to one another . • Geometers make use of the following technical words , ' to signify certain ways of changing either the order or ... Page 104

Invertendo , by inversion ; when there are four

Invertendo , by inversion ; when there are four

**proportionals**, and it is inferred , that the second is to the first as the fourth to the third . Prop . B. Book 5 . XV . Componendo , by composition ; when there are four**proportionals**... Page 111

... or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore if the first , & c . Q. E. D. PROP . B. THEOR . If four magnitudes are

... or less than it , the third can be proved to be equal to the fourth , or less than it . Therefore if the first , & c . Q. E. D. PROP . B. THEOR . If four magnitudes are

**proportionals**, they are propor- See N. tionals also ... Page 117

Let any number of magnitudes A , B , C , D , E , F , be

Let any number of magnitudes A , B , C , D , E , F , be

**proportionals**; that is , as A is to B , so C to D , and E to F : as A is to B , so shall A , C , E together be to B , D , F together . Take of A , C , E any G equimultiples ...### 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