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 109
... ratio than the third magnitude has to the fourth : and , on the contrary , the third is said to have to the fourth a less ratio than the first has to the second . VIII . • When there is any number of magnitudes greater than two , of ...
... ratio than the third magnitude has to the fourth : and , on the contrary , the third is said to have to the fourth a less ratio than the first has to the second . VIII . • When there is any number of magnitudes greater than two , of ...
Página 206
... ratio compounded of the ratios of the bases " AC and GK , and of the altitudes AE and GM ; therefore also the solids Y and Z have to one another a ratio that is compounded of the same ratios . Therefore , & c . Q. E. D. COR . 1. Hence ...
... ratio compounded of the ratios of the bases " AC and GK , and of the altitudes AE and GM ; therefore also the solids Y and Z have to one another a ratio that is compounded of the same ratios . Therefore , & c . Q. E. D. COR . 1. Hence ...
Página 208
... ratio of the solid AG to the solid KQ is com pounded of the ratios of AC to KM , and of AE to KO . Now , the ratio of AC to KM , because they are equiangular parallelograms , is compounded ( 23. 6. ) of the ratios of AB to KL , and of ...
... ratio of the solid AG to the solid KQ is com pounded of the ratios of AC to KM , and of AE to KO . Now , the ratio of AC to KM , because they are equiangular parallelograms , is compounded ( 23. 6. ) of the ratios of AB to KL , and of ...
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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