## 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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**Propositions**, as well as their Demonstra- tions , to Theon ; others think the**Propositions**to be Euclid's , but that the Demonstrations are Theon's ; and others main- tain , that all the**Propositions**and their Demonstrations are ... Page 8

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**Proposition**is a Theo- rem , not a Definition ; because the equality of figures of any kind must be demonstrated , and not assumed ; and there- fore , though this were a true**Proposition**, it ought to have been demonstrated . But ... Page 9

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**Proposition**18th of the 12th Book , depend upon the 9th Definition of the 11th Book , which is not a right ...**Propositions**have , for these reasons , been insufficiently demonstrated since Theon's time hitherto . Besides , there are ... Page 10

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**Proposition**concerning a property of quadrilateral figures in a circle is added at the end of the sixth Book . Also the Note on the 29th Proposi- tion , Book 1st , is altered , and made more explicit , and a more general Demonstration ... Page 12

... at length meet upon that side on which " are the angles which are less than two right angles . See " the notes on prop . 29. of Book I. "

... at length meet upon that side on which " are the angles which are less than two right angles . See " the notes on prop . 29. of Book I. "

**PROPOSITION**I. PROBLEM . To describe an equilateral triangle upon 12 BOOK I. THE ELEMENTS OF EUCLID.### 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