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 ix
... manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another , one of them greater , and another less than the space contained within the circle . In the Second Book ...
... manner , the quadrature of the circle is performed only by approximation , or by finding two rectangles nearly equal to one another , one of them greater , and another less than the space contained within the circle . In the Second Book ...
Página x
... manner of doing which he has not previously ex- plained . Now , the only use of this rule is to prevent the admission of impossible or contradictory supposi- tions , which no doubt , might lead into error ; and it is a rule well ...
... manner of doing which he has not previously ex- plained . Now , the only use of this rule is to prevent the admission of impossible or contradictory supposi- tions , which no doubt , might lead into error ; and it is a rule well ...
Página xi
... evidently possible , though the manner of actually describing them may not have been explained . In this way , I have been enabled to offer that very refined artifice in geometri- cal reasoning , to which we give the name of PREFACE . xi.
... evidently possible , though the manner of actually describing them may not have been explained . In this way , I have been enabled to offer that very refined artifice in geometri- cal reasoning , to which we give the name of PREFACE . xi.
Página 30
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q E. D. PROP . XV . THEOR . If two straight lines ...
... manner , it may be demonstrated , that no other can be in the same straight line with it but BD , which therefore is in the same straight line with CB . Wherefore , if at a point , & c . Q E. D. PROP . XV . THEOR . If two straight lines ...
Página 31
... manner may be demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the ...
... manner may be demonstrated that the angles CEB , AED are equal . There- fore , if two straight lines , & c . Q. E. D. COR . 1. From this it is manifest , that if two straight lines cut one another , the angles which they make at the ...
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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