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 σελίδες |
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Σελίδα 48
... parallelogram that shall be equal to the given triangle ABC , and have one of its angles equal to D. F G Bisect ( 10. 1. ) BC in E , join AE , and at the point E in the straight line EC make ( 23 . 1. ) the angle CEF equal to D ; and ...
... parallelogram that shall be equal to the given triangle ABC , and have one of its angles equal to D. F G Bisect ( 10. 1. ) BC in E , join AE , and at the point E in the straight line EC make ( 23 . 1. ) the angle CEF equal to D ; and ...
Σελίδα 125
... parallelogram CE is double of the triangle ABC ( 41. 1. ) , and the parallelogram CF double of the triangle AOD , and because magnitudes have the same ratio which their equimultiples have ( 15. 5. ) ; as the triangle ABC is to the ...
... parallelogram CE is double of the triangle ABC ( 41. 1. ) , and the parallelogram CF double of the triangle AOD , and because magnitudes have the same ratio which their equimultiples have ( 15. 5. ) ; as the triangle ABC is to the ...
Σελίδα 145
... parallelogram CH ( 1. 6. ) ; and as BC to CG , so is K to L ; therefore K is ( 11. 5. ) to L , as the parallelogram AC to the pa- rallelogram CH : again , because as DC to CE , so is the parallelogram CH to the parallelogram CF : aud as ...
... parallelogram CH ( 1. 6. ) ; and as BC to CG , so is K to L ; therefore K is ( 11. 5. ) to L , as the parallelogram AC to the pa- rallelogram CH : again , because as DC to CE , so is the parallelogram CH to the parallelogram CF : aud as ...
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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