## The Elements of Euclid |

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Page 120

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 se• cond , as the third to the fourth . ” VII . Page 121

In

In

**proportionals**, the antecedent terms are called homologous to one another , as also the consequents to one anothier . Geometers make use of the following technical words to sig . nify certain ways of changing either the order or ... Page 122

Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many others , so that they are

Ex æquali ( sc . distantia ) , or ex æquo , from equality of distance ; when there is any number of magnitudes more than two , and as many others , so that they are

**proportionals**when taken two and two of each rank , and it is inferred ... Page 129

... 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 be

... 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 be

**proportionals**, they are pro- See Note . portionals also when ... Page 136

... K are any equimultiples whatever of A , E , and L , N any whatever of B , F : therefore , as A is to B , so is E to Fa . Wherefore ratios that , & c . Q.F.D. 534 PROP . XII . THEOR . any number of magnitudes be

... K are any equimultiples whatever of A , E , and L , N any whatever of B , F : therefore , as A is to B , so is E to Fa . Wherefore ratios that , & c . Q.F.D. 534 PROP . XII . THEOR . any number of magnitudes be

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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