## 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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**PROPOSITION**I. PROBLEM . To describe an equilateral triangle upon a given finite straight line . Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From the centre A , at the distance AB ... Page 33

... the straight lines AB , CD , if produced far enough , shall meet ; but they never meet , since they are parallel * See the Notes to this

... the straight lines AB , CD , if produced far enough , shall meet ; but they never meet , since they are parallel * See the Notes to this

**Proposition**. E by the hypothesis ; therefore the angle AGH is not BOOK I. 33 THE ELEMENTS OF EUCLID . Page 53

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**proposition**it is manifest , that the difference of the squares of two unequal lines AC , CD , is equal to the rectangle contained by their sum and difference . PROP . VI . THEOR . Ir a straight line BOOK II . 53 THE ELEMENTS OF EUCLID . Page 110

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**proposition**, be in the points A , B , C , D , E , so that the cir- cumferences AB , BC , CD , DE , EA are equal ( 11. 4. ) ; and through the points A , B , C , D , E draw GH , HK , KL , LM , MG , touching ( 17. 3. ) the circle ; take ... Page 132

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**proposition**, there are some equimultiples of A and B , and some multiple of C such , that the multiple of A is greater than the multiple of C , but the multiple of B is not greater than that of C. Let such multiples be taken , and let ...### 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 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.