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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 páginas |
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Página 71
... passes through the centre , is equal to one more re- mote , which is impossible . Therefore , if any point be taken ... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes ...
... passes through the centre , is equal to one more re- mote , which is impossible . Therefore , if any point be taken ... passes through the centre ; of those which fall upon the concave circumference , the greatest is that which passes ...
Página 72
... passes through the centre . Of those which fall upon the concave part of the circumference AEFC , the greatest is AD which passes through the centre ; and the line nearer to AD is always greater than the more remote , viz . DE than DF ...
... passes through the centre . Of those which fall upon the concave part of the circumference AEFC , the greatest is AD which passes through the centre ; and the line nearer to AD is always greater than the more remote , viz . DE than DF ...
Página 73
... straight line which joins their centres being produced , will pass through the point of contact . Let the two circles ABC , ADE , touch each other internally in the K point A , and let F be the centre of OF GEOMETRY . 73 BOOK III . 123.
... straight line which joins their centres being produced , will pass through the point of contact . Let the two circles ABC , ADE , touch each other internally in the K point A , and let F be the centre of OF GEOMETRY . 73 BOOK III . 123.
Página 74
... pass through A. Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . If two circles touch each other externally , the straight line which joins their centres will pass through the point of contact . Let the two circles ABC ...
... pass through A. Therefore , if two circles , & c . Q. E. D. PROP . XII . THEOR . If two circles touch each other externally , the straight line which joins their centres will pass through the point of contact . Let the two circles ABC ...
Página 75
... passes through the point of contact ( 11.3 . ) ; but it does not pass through it , because the points B , D are without the straight line GH , which is absurd : Therefore one circle cannot touch another in the inside in more points than ...
... passes through the point of contact ( 11.3 . ) ; but it does not pass through it , because the points B , D are without the straight line GH , which is absurd : Therefore one circle cannot touch another in the inside in more points than ...
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Términos y frases comunes
ABC is equal ABCD altitude angle ABC angle ACB angle BAC angle EDF arch AC base BC bisected centre circle ABC circumference cosine cylinder 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 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