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 54
... square of the whole line . A C B Let the straight line AB be divided into any two parts in the point C ; the rectangle AB BC , together with the rect- angle AB.AC , is equal to the square of AB ; or AB.AC + AB . BC = : AB2 . On AB ...
... square of the whole line . A C B Let the straight line AB be divided into any two parts in the point C ; the rectangle AB BC , together with the rect- angle AB.AC , is equal to the square of AB ; or AB.AC + AB . BC = : AB2 . On AB ...
Página 55
... square CDEB , and produce ED to F , and through A draw ( 31. 1. ) AF parallel to CD or BE ; then AE = AD + CE . But ... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by ...
... square CDEB , and produce ED to F , and through A draw ( 31. 1. ) AF parallel to CD or BE ; then AE = AD + CE . But ... square of the whole line is equal to the squares of the two parts , together with twice the rectangle contained by ...
Página 56
... square of the line between the points of section , is equal to the square of half the line . the Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts in the point D ; the rectangle AD.DB ...
... square of the line between the points of section , is equal to the square of half the line . the Let the straight line AB be divided into two equal parts in the point C , and into two unequal parts in the point D ; the rectangle AD.DB ...
Página 57
... square of CB , is equal to the square of CD . Upon CD describe ( 46. 1. ) the square CEFD , join DE , and through B draw ( 31. 1 ) BHG parallel to CE or DF , and through H draw KLM parallel to AD or EF , and also through A draw AK ...
... square of CB , is equal to the square of CD . Upon CD describe ( 46. 1. ) the square CEFD , join DE , and through B draw ( 31. 1 ) BHG parallel to CE or DF , and through H draw KLM parallel to AD or EF , and also through A draw AK ...
Página 58
... square of the difference of the lines . " PROP . VIII . THEOR . If a straight line be divided into any two parts , four times the rectangle contained by the whole line , and one of the parts , together with the square of the other part ...
... square of the difference of the lines . " PROP . VIII . THEOR . If a straight line be divided into any two parts , four times the rectangle contained by the whole line , and one of the parts , together with the square of the other part ...
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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