## 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 311

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**given**in that book , as in this but indeed there is scarce any need of it in either of them : though I think that a ...**species**of compound ratio . But Theon has made it the 5th def . of book 6. where he gives an absurd and entirely ... Page 365

... given , when a ratio of a given magnitude to a given magnitude which is the same ratio with it can be found . III . Rectilineal figures are said to be

... given , when a ratio of a given magnitude to a given magnitude which is the same ratio with it can be found . III . Rectilineal figures are said to be

**given in species**, which have each of their angles given , and the ratios of their ... Page 394

... given ( 1. dat . ) : but as LM to MN , so is GH to HK ; wherefore the ratio of GH to HK is given . 39 . PROP . XLII . Ir each of the sides of a triangle be given in magnitude , the triangle is

... given ( 1. dat . ) : but as LM to MN , so is GH to HK ; wherefore the ratio of GH to HK is given . 39 . PROP . XLII . Ir each of the sides of a triangle be given in magnitude , the triangle is

**given in species**. Let each of the sides of ... Page 395

... given and the points D , E are given ; therefore each of the straight lines . DE , EF , FD is given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

... given and the points D , E are given ; therefore each of the straight lines . DE , EF , FD is given ( 29. dat . ) in magnitude ; wherefore the triangle DEF is

**given in species**( 42. dat . ) ; and it is similar ( 4. 6. 1. def . 6. ) to ... Page 396

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**given in species**. Let the sides of the triangle ABC have given ratios to one another , the triangle ABC is**given in species**. B A DE F C G Take a straight line D given in magnitude ; and because the ratio of AB to BC is given , make ...### 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.