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 TrigonometryCollins & Hannay, 1860 - 333 páginas |
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Página 52
... square GB : And in the same manner , by joining AE , BK , it is demonstrated that the parallelogram CL is equal to the square HC . Therefore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is de ...
... square GB : And in the same manner , by joining AE , BK , it is demonstrated that the parallelogram CL is equal to the square HC . Therefore , the whole square BDEC is equal to the two squares GB , HC ; and the square BDEC is de ...
Página 61
... square ABDC ; bisect ( 10. 1. ) AC in E , and join BE ; produce CA to F , and make ( 3. 1. ) EF equal to EB , and upon AF describe ( 46. 1. ) the square FGHA , AB is divided in H , so that the rectangle AB , BH is equal to the square of ...
... square ABDC ; bisect ( 10. 1. ) AC in E , and join BE ; produce CA to F , and make ( 3. 1. ) EF equal to EB , and upon AF describe ( 46. 1. ) the square FGHA , AB is divided in H , so that the rectangle AB , BH is equal to the square of ...
Página 164
... square of AB to the square of GH ; but be- cause the triangles ANB , GOH are equiangular , the square of AB is to the square of GH as the square of AN to the square of GO ( 4. 6. ) , or as four times the square of AN to four times the ...
... square of AB to the square of GH ; but be- cause the triangles ANB , GOH are equiangular , the square of AB is to the square of GH as the square of AN to the square of GO ( 4. 6. ) , or as four times the square of AN to four times 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 and similar 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 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 side BC sine solid angle solid parallelopipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore