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 TrigonometryE. Duyckinck, and George Long, 1824 - 333 σελίδες |
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Σελίδα 38
... AB is not unequal to DE , that is , it is equal to it ; and BC is equal to EF ; therefore the two AB , BC are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF , therefore the base AC is equal ( 4. 1 ...
... AB is not unequal to DE , that is , it is equal to it ; and BC is equal to EF ; therefore the two AB , BC are equal to the two DE , EF , each to each ; and the angle ABC is equal to the angle DEF , therefore the base AC is equal ( 4. 1 ...
Σελίδα 41
... equal ( 29. 1. ) to the angle GKD ; and it was shewn that the angle AGK is equal to the angle GHF ; therefore also ... ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior ...
... equal ( 29. 1. ) to the angle GKD ; and it was shewn that the angle AGK is equal to the angle GHF ; therefore also ... ABC be a triangle , and let one of its sides BC be produced to D ; the exterior angle ACD is equal to the two interior ...
Σελίδα 42
... equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the ...
... equal to the interior and opposite angle ABC ; but the angle ACE was shewn to be equal to the angle BAC ; therefore the whole exteri- or angle ACD is equal to the two interior and opposite angles CAB , ABC ; to these angles add the ...
Σελίδα 43
... equal and parallel straight lines , towards the same parts , are also themselves equal and parallel . Let AB , CD ... ABC , BCD are equal ( 29. 1. ) ; and because AB is equal to CD , and BC common to the two triangles ABC , DCB , the two ...
... equal and parallel straight lines , towards the same parts , are also themselves equal and parallel . Let AB , CD ... ABC , BCD are equal ( 29. 1. ) ; and because AB is equal to CD , and BC common to the two triangles ABC , DCB , the two ...
Σελίδα 44
... equal to one another ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ABC is equal to the angle BCD ; therefore the triangle ABC is ...
... equal to one another ; also , its diameter bisects it ; for AB being equal to CD , and BC common , the two AB , BC are equal to the two DC , CB , each to each ; now the angle ABC is equal to the angle BCD ; therefore the triangle ABC is ...
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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 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 parallelepipeds 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 shewn side BC sine solid angle solid parallelepipeds spherical angle spherical triangle straight line AC THEOR third touches the circle triangle ABC triangle DEF wherefore