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

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Page 126

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**Ratio**a mutual relation of two magnitudes “ of the same kind to one another , in respect • of quantity . ” IV . Magnitudes are said to have a**ratio**to one another , when the less can be multiplied so as to exceed the other . Page 127

V. The first of four magnitudes is said to have the same

V. The first of four magnitudes is said to have the same

**ratio**to the second , which the third has to the fourth , when any equimultiples whatsoever of the first and third being taken , and any equimultiples whatsoever of the second and ... Page 128

X. When three magnitudes are proportionals , the first is said to have to the third the duplicate

X. When three magnitudes are proportionals , the first is said to have to the third the duplicate

**ratio**of that which it has to the second . XI . When four magnitudes are continual proportionals , the first is said to have to the fourth ... Page 129

6 6 : D ; then , for shortness sake , M is said to have to N the

6 6 : D ; then , for shortness sake , M is said to have to N the

**ratio**compounded of the**ratios**of E to F , G to H , and K to L. XII . In proportionals , the antecedent terms are called homologous to one another , as also the ... Page 134

If the first of four magnitudes has the same

If the first of four magnitudes has the same

**ratio**to the second which the third has to the fourth ; then any equimultiples whatever of the first and third shall have the same**ratio**to any equimultiples of the second and fourth , vis .### 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 |

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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