## Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle and the Geometry of Solids ; to which are Added Elements of Plane and Spherical Trigonometry |

### From inside the book

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... besides these , are called Trapeziums . XXX . Parallel straight lines , are such as are in the same plane , and which being

... besides these , are called Trapeziums . XXX . Parallel straight lines , are such as are in the same plane , and which being

**produced**ever so far both ways , do not meet . POSTULATES . I. LET it be granted that a straight 20 ELEMENTS 00 ... Page 21

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**produced**to any length in a straight line . III . And that a circle may be described from any centre , at any distance from that centre . AXIOMS . I. THINGS which are equal to the same thing are equal to one another . II . If equals be ... Page 24

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**produced**, the angles upon the other side of the base shall also be equal . Let ABC be an isosceles triangle , of which the side AB is equal to AC , and let the straight lines AB , AC be**produced**to D and E , the angle ABC shall be ... Page 26

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**produce**AC , AD to E , F ; therefore , because AC is equal to AD in the triangle F C D ACD , the angles ECD , FDC upon the other side of the base CD are equal ( 5. 1. ) to one ano- ther but the angle ECD is greater than the angle BCD ... Page 29

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**produced**to any length both ways , and let C be a point without it . It is required to draw a straight line perpendi- C cular to AB from the point C. Take any point D upon the other side of AB , and from the : E centre C , at the ...### Other editions - View all

### Common terms and phrases

ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder definition demonstrated diameter draw equal angles equiangular equilateral equilateral polygon equimultiples Euclid exterior angle fore four right angles given straight line greater hypotenuse inscribed join less Let ABC Let the straight line BC magnitudes MDCCCXX meet multiple opposite angle parallel parallelepipeds parallelogram perpendicular polygon prism PROB produced proportionals proposition Q. E. D. COR Q. E. D. PROP radius ratio rectangle contained rectilineal figure remaining angle segment semicircle shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore