## The Elements of Euclid: Viz. the First Six Books, Together with the Eleventh and Twelfth. The Errors, by which Theon, Or Others, Have Long Ago Vitiated These Books, are Corrected, and Some of Euclid's Demonstrations are Restored. Also, the Book of Euclid's Data, in Like Manner Corrected |

### From inside the book

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**multiple**of a less , when the greater is measured by the less , that is , when the greater contains the less a ...**multiple**of the third is also less than that of the fourth ; or , if the**multiple**of the first be equal to that of the ... Page 118

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**multiple**of the first is greater than that of the second , but the**multiple**of the third is not greater than the**multiple**of the fourth ; then the first is said to have to the second a greater ratio than the third magnitude has to the ... Page 121

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**multiple**is greater than the same**multiple**of another , is greater than that other magnitude . PROP . I. THEOR . Ir any number of magnitudes be equimultiples of as many , each of each ; what**multiple**soever any one of them is of its ... Page 122

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**multiple**of the se- cond that the third is of the fourth , and the fifth the same**multiple**of the second that the sixth is of the fourth ; then shall the first together with the fifth be the same**multiple**of the second , that the third ... Page 123

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**multiple**of B the second , that C the third is of D the fourth ; and of A , C let the equimultiples EF , GH be taken ; then EF is the same**multiple**of B , that GH is of D. Because EF is the same**multiple**of A , that GH is of C , there ...### Other editions - View all

The Elements of Euclid: Viz, the First Six Books, Together with the Eleventh ... Robert Simson,Euclid Euclid No preview available - 2018 |

### Common terms and phrases

altitude angle ABC angle BAC base BC BC is equal BC is given bisected centre circle ABCD circumference cone cylinder demonstrated described diameter draw drawn equal angles equiangular equimultiples Euclid ex æquali excess fore given angle given in magnitude given in position given in species given magnitude given ratio given straight line gnomon greater join less Let ABC meet multiple parallel parallelogram parallelogram AC perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius ratio of AE rectangle CB rectangle contained rectilineal figure remaining angle right angles segment sides BA similar sine solid angle solid parallelopipeds square of AC straight line AB straight line BC tangent THEOR third triangle ABC triplicate ratio vertex wherefore