## Elements of Geometry: Containing the First Six Books of Euclid: With a Supplement ... to which are Added, Elements of Plane and Sphericale Trigonometry ... From the Last London Ed., Enl |

### From inside the book

Results 1-5 of 97

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**parallel**lines . In the third Book , the re- marks concerning the angles made by a straight line , and the circumference of a circle , are left out , as tending to perplex one who has advanced no farther than the elements of the science ... Page 6

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**parallel**lines ) , is the sign of equality ; thus , A = B , implies that the quantity denoted by A is equal to the quantity denoted by B , and is read A equal to B. = 19. To signify that A is greater than B , the expression A7B is used ... Page 11

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**Parallel**straight lines are such as are in the same plane , and which being produced ever so far both ways , do not meet . POSTULATES . 1. LET it be granted that a straight line may be drawn from any one point to any other point . 2 ... Page 27

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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 . For , if it be not**parallel**, AB and CD being produced shall meet ... Page 28

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**parallel**to CD . COR . Hence , when two straight lines are perpendicular to a third line , they will be**parallel**to each other . PROP . XXIX . THEOR . If a straight line fall upon two**parallel**straight lines , it makes the alternate ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD adjacent angles altitude angle ABC angle ACB angle BAC base BC bisected centre chord circle ABC circumference cosine cylinder demonstrated described diameter divided draw equal and similar equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given rectilineal given straight line greater Hence hypotenuse inscribed join less Let ABC Let the straight magnitudes meet multiple opposite angle parallel parallelogram parallelopiped perpendicular polygon prism PROB PROP proportional proposition quadrilateral radius ratio rectangle contained rectilineal figure remaining angle right angled triangle SCHOLIUM segment semicircle shewn side BC sine solid angle solid parallelopiped spherical angle spherical triangle square straight line BC THEOR touches the circle triangle ABC triangle DEF wherefore