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 40
... equal to two right angles . For if AGH be not equal to GHD , let KG be drawn making the angle KGH equal to GHD , and produce KG to L ; then KL will be parallel to CD ( 27. 1. ) ; but E AB is also parallel to CD ; therefore two straight ...
... equal to two right angles . For if AGH be not equal to GHD , let KG be drawn making the angle KGH equal to GHD , and produce KG to L ; then KL will be parallel to CD ( 27. 1. ) ; but E AB is also parallel to CD ; therefore two straight ...
Σελίδα 41
... equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. A Ꮐ B E I T K D PROP . XXXI . PROB . To draw a ...
... equal to the angle GHF ; therefore also AGK is equal to GKD ; and they are alternate angles ; therefore AB is parallel ( 27.1 . ) to CD . Where- fore straight lines , & c . Q. E. D. A Ꮐ B E I T K D PROP . XXXI . PROB . To draw a ...
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 . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD are also equal and parallel . Join BC ; and because AB is pa- rallel to CD , and BC ...
... equal and parallel . Let AB , CD , be equal and parallel straight lines , and joined towards the same parts by the straight lines AC , BD ; AC , BD are also equal and parallel . Join BC ; and because AB is pa- rallel to CD , and BC ...
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