## 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 |

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**perpendicular**to a given straight line , of an unlimited length , from a given point without it . Let AB be a given straight line , which may be produced to any length both ways , and let C be a point without it . It is required to draw ... Page 62

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**perpendicular**falls , and the straight line intercepted betweeen the**perpendicular**and the obtuse angle . Let ABC be an obtuse angled triangle , having the obtuse angle ACB , and from the point A let AD be drawn ( 12. 1. )**perpendicular**... Page 63

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**perpendicular**and the acute angle at B ; and it is manifest that ( 47. 1. ) AB + BC = AC2 + 2BC2 = AC2 + 2BC.BC . Therefore in every triangle , & c . Q. E. D. A PROP . XIV . PROB . B To describe a square that shall be equal to a given ... Page 64

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**perpendicular**to BC , and because BEA is a right angle , AB2 = ( 47. 1. ) BE 2+ AE2 and AC2 = CE2 + AE2 ; wherefore AB2 + AC2 = BE + CE2 + 2AE2 . But be- cause the line BC is cut equally in D , and unequally in E , BE + CE2 = ( 9.2 ... Page 66

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**perpendicular**falls , is said to be farther from the centre B. An arch of a circle is any part of the circumference . V. A segment of a circle is the figure con- VI . An angle in a segment is the angle. tained by a straight line , and ...### 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