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

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Page 127

Magnitudes which have the same ratio are called

Magnitudes which have the same ratio are called

**proportionals**. ' N. B. When four mag' nitudes are**proportionals**, it is usually ex. pressed by saying , the first is to the second , as the third to the fourth . ' 6 VII . Page 128

X. When three magnitudes are

X. When three magnitudes are

**proportionals**, the first is said to have to the third the duplicate ratio of that which it ... and so on , quadruplicate , & c . increasing the denomination still by unity , in any number of**proportionals**. Page 129

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 130

Convertendo , by conversion ; when there are four

Convertendo , by conversion ; when there are four

**proportionals**, and it is inferred , that the first is to its excess above the second , as the third to its excess above the fourth . Prop . E. Book 5 . XVIII . Page 138

If four magnitudes are

If four magnitudes are

**proportionals**, they are**proportionals**also when taken inversely . Let A be to B , as C is to D : then also inversely B shall be to A , as D to C. Take of B and D any equimultiples whatever E and F ; and of A and ...### 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