## 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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**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 144

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**ex æquali**, " or " ex æquo . First , Let there be three magnitudes A , B , C , and as many * See Note . 1 others D , E , F , which , taken 144 BOOK V. THE ELEMENTS OF EUCLID . Page 146

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**ex æquali**in proportione perturbata ; " or , " ex æquo pertur bato . " * First , Let there be three magnitudes A , B , C , and other three D , E , F , which , taken two and two in a cross order , have the same ratio , that is , such ... Page 147

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**ex æquali**( 22. 5. ) , AB is to BG , as DE to EH : and because these mag- nitudes are proportionals , they shall likewise be proportionals when taken B. E- H 1.1 jointly ( 18. 5. ) as , therefore , AG is to GB , so is DH to HE ; but as ... Page 149

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**ex æquali**, A is to C , as D to F ( 22. 5. ) A. B. C. D. E. F. Next , Let A be to B , as E to F , and B to C , as D to E ; there- fore ,**ex æquali**in proportione perturbata ( 23. 5. ) , A is to C , as D to F ; that is , the ratio of A ...### 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