## 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 |

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Viz. the First Six Books, Together

Viz. the First Six Books, Together

**with**the Eleventh and Twelfth. The Errors, by which ...**given**; and by taking out of this Book , besides other things , the good ...**magnitude**. " Now this Proposition is a Theo- rem , not a Definition ... Page 313

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**given**the method of doing . For this reason , we have A changed the construction to one , which , without doubt , is Euclid's , in which nothing is required but to add a**magnitude**to itself a certain number of times ; and this is to be ... Page 318

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**given**the demonstration of the 10th proposition as we now have it , instead of that which Eudoxus or Euclid had**given**, has been deceived in applying what is manifest , when understood of**magnitudes**, unto ratios , viz . that a**magnitude**... Page 336

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**given**straight line AB the rectangle AP has been applied equal to the**given**rectangle C , D , exceeding by the ...**magnitude**of it being likewise**given**, to find its sides . And the fourth problem is the same**with**this . To find the ... Page 339

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**magnitude**, that are neither similar nor equal , as shall be demonstrated ...**Magnitudes**that wholly coincide , are equal to one another : " or from prop . A. of ...**given**no definition of equal figures , and it is certain he did not**give**...### 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