## The Elements of Euclid: viz. the first six books, together with the eleventh and twelfth; and also the book of Euclid's Data |

### From inside the book

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Page 11

... besides these are call- ed trapeziums . XXXV .

... besides these are call- ed trapeziums . XXXV .

**Parallel**straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . A POSTULATES . I. LET it be granted that a straight 4 THE ELEMENTS. Page 25

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**parallel**. Let the straight line EF , which falls upon the two straight lines AB , CD , make the alternate angles AEF , EFD equal to one another ; AB is**parallel**to CD . Book I. For , if it be not**parallel**, AB and CD being produced ... Page 26

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**parallel**to CD . Wherefore , " if a straight line , ” & c . Q. E. D. See the notes on this propo- sition . a 13. 1 . PROP . XXIX . THEOR . If a straight line fall upon two**parallel**straight lines , it makes the alternate angles equal to ... Page 27

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**parallel**to the same straight line are**parallel**to one another . Let AB , CD be each of them**parallel**to EF , AB is also**parallel**to CD . Let the straight line GHK cut AB , EF , CD ; and because GHK cuts the**parallel**straight a lines AB ... Page 28

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**parallel**to the given straight line BC . Which was to be done . a 31. 1 . b 29. 1 . PROP . XXXII . THEOR . If a side ...**parallel**to the straight line AB ; and be- cause AB is**parallel**to CE and AC meets them , the al- ternate ...### Other editions - View all

The Elements Of Euclid: Viz. The First Six Books, Together With The Eleventh ... Robert Simson,Euclid,John Davidson No preview available - 2019 |

### Common terms and phrases

ABCD altitude angle ABC angle BAC arch base BC BC is equal BC is given bisected Book XI centre circle ABC circumference cone cosine 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 gles gnomon greater half the perimeter hypotenuse join less Let ABC multiple parallel parallelogram perpendicular point F polygon prism proportionals proposition Q. E. D. PROP radius rectangle CB rectangle contained rectilineal figure remaining angle right angles segment side BC similar sine solid angle solid parallelepiped spherical angle square of AC straight line AB straight line BC tangent THEOR tiple triangle ABC vertex wherefore

### Popular passages

Page 95 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.

Page 153 - 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 306 - Again ; the mathematical postulate, that " things which are equal to the same are equal to one another," is similar to the form of the syllogism in logic, which unites things agreeing in the middle term.

Page 11 - A circle is a plane figure contained by one line, which is called the circumference, and is such that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.

Page 11 - Upon the same base, and on the same side of it, there cannot be two triangles that have their sides which are terminated in one extremity of the base equal to one another, and likewise those which are terminated in the other extremity.

Page 317 - Equiangular parallelograms have to one another the ratio which is compounded of the ratios of their sides.

Page 54 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...

Page 26 - IF a straight line fall upon two parallel straight lines it makes the alternate angles equal to one another ; and the exterior angle equal to the interior and opposite, upon the same side ; and likewise the two interior angles upon the same side together equal to two right angles.

Page 11 - If a straight line meet two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...

Page 93 - A circle is said to be described about a rectilineal figure, when the circumference of the circle passes through all the angular points of the figure about which it is described. VII. A straight line is said to be placed in a circle, when the extremities of it are in the circumference of the circle.