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 37
... angle BAC is not equal to the angle EDF ; neither is it less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; there- fore the angle BAC is not less than the angle EDF : and it was shewn that it is ...
... angle BAC is not equal to the angle EDF ; neither is it less ; because then the base BC would be less ( 24. 1. ) than the base EF ; but it is not ; there- fore the angle BAC is not less than the angle EDF : and it was shewn that it is ...
Σελίδα 80
... angle BDC is double of the angle BAC . First , let D , the centre of the circle , be within the angle BAC , and join AD , and produce it to E : Because DA is equal to DB , the anglo DAB is equal ( 5. 1. ) to the angle DBA : therefore the ...
... angle BDC is double of the angle BAC . First , let D , the centre of the circle , be within the angle BAC , and join AD , and produce it to E : Because DA is equal to DB , the anglo DAB is equal ( 5. 1. ) to the angle DBA : therefore the ...
Σελίδα 151
... angle CDE is equal to the angle ACD ; wherefore also BAC is equal to CDE : And because the triangles ABC , DCE have one angle at A equal to one at D , B D C E and the sides about these angles proportionals , viz . BA to AC , as CD to DE ...
... angle CDE is equal to the angle ACD ; wherefore also BAC is equal to CDE : And because the triangles ABC , DCE have one angle at A equal to one at D , B D C E and the sides about these angles proportionals , viz . BA to AC , as CD to DE ...
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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