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 99
... manner , it may be demonstrated , that GH , GK , are each of them equal to FG or GE , there- fore the four straight lines , E , GF , GH , GK , are equal to one another ; and the circle described from the centre G , at the distance of ...
... manner , it may be demonstrated , that GH , GK , are each of them equal to FG or GE , there- fore the four straight lines , E , GF , GH , GK , are equal to one another ; and the circle described from the centre G , at the distance of ...
Σελίδα 104
... manner , it may be demon- strated that the angles BAE , AED , are bisected by the straight lines AF , EF : from the point F draw ( 12. 1. ) FG , FH , FK , FL , FM per- pendiculars to the straight lines AB , BC , CD , DE , EA : and ...
... manner , it may be demon- strated that the angles BAE , AED , are bisected by the straight lines AF , EF : from the point F draw ( 12. 1. ) FG , FH , FK , FL , FM per- pendiculars to the straight lines AB , BC , CD , DE , EA : and ...
Σελίδα 253
... manner , D is the pole of BC , and E the pole of AB . K F N M B G H And since F , E are the poles of AL , AM , the arches FL and EM ( 2. ) are quadrants , and FL , EM together , that is , FE and ML toge- ther , are equal to a semicircle ...
... manner , D is the pole of BC , and E the pole of AB . K F N M B G H And since F , E are the poles of AL , AM , the arches FL and EM ( 2. ) are quadrants , and FL , EM together , that is , FE and ML toge- ther , are equal to a semicircle ...
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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