## 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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**demonstrated**, and not assumed ; and there- fore , though this were a true Proposition , it ought to have been**demonstrated**. But , indeed , this Proposition , which makes the 10th Definition of the 11th Book , is not true universally ... Page 9

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**demonstrated**since Theon's time hitherto . Besides , there are several other things , which have nothing of Euclid's accuracy , and which plainly show , that his Elements have been much corrupted by unskilful geometers ; and , though ... Page 15

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**demonstrated**. PROP . V. THEOR . THE angles at the base of an isosceles triangle are equal . to one another : and , if the equal sides be produced , the angles upon the other side of the base shall be equal . Let ABC be an isosceles ... Page 16

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**demonstrated**, that the whole angle ABG is equal to the whole ACF , the parts of which , the angles CBG , BCF are also equal ; the remaining angle ABC is therefore equal to the remaining angle ACB , which are the angles at the base of ... Page 20

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**demonstrated**, that two straight lines cannot have a common segment . If it be possible , let the two straight lines ABC , ABD have the segment AB common to both of them . From the point B draw BE at right angles to AB ; and because ABC ...### 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