## 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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Page 119

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**excess**of the first above the second , is to the second , as the**excess**of the third above the fourth , is to the fourth . 17th Prop . book 5 . XVII . Convertendo , by conversion ; when there are four proportionals , and it is inferred ... Page 120

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**excess**above the fourth . Prop . E , book 5 . XVIII . 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 ... Page 142

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**excess**above the second , as the third to its**excess**above the fourth . Let AB be to BE , as CD to DF ; then BA is to A AE , as DC to CF. Because AB is to BE , as CD to DF , by divi- sion ( 17. 5. ) , AE is to EB , as CF to FD , and by ... Page 148

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**excess**of the first and fifth shall be to the second , as the**excess**of the third and sixth to the fourth . The demon- stration of this is the same with that of the proposition , if divi- sion be used instead of composition . COR . 2 ... Page 184

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**excess**of EF above C , and similar and similarly situated to D ; but D is similar to EF , therefore ( 21. 6. ) also KM is similar to EF ; let KL * See Note . be the homologous side to EG , and LM , 184 BOOK VI . THE ELEMENTS OF EUCLID .### Other editions - View all

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2018 |

The Elements of Euclid, Viz: The Errors, by Which Theon, Or Others, Have ... Robert Simson,Robert Euclid No preview available - 2015 |

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 co-sine 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 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

### Popular passages

Page 9 - Let it be granted that a straight line may be drawn from any one point to any other point.

Page 81 - The angles in the same segment of a circle are equal to one another.

Page 315 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 33 - All the interior angles of any rectilineal figure, together with four right angles, are equal to twice as many right angles as the figure has sides.

Page 49 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.

Page 96 - If from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.

Page 155 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.

Page 22 - ANY two angles of a triangle are together less than two right angles.

Page 25 - Let A, B, C be the three given straight lines, of which any two whatever are greater than the third, viz.

Page 24 - Any two sides of a triangle are together greater than the third side.