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
... parallel to CD ( 27. 1. ) ; but E AB is also parallel to CD ; therefore two straight lines G are drawn through the same point G , parallel to CD , and K yet not coinciding with one an- other , which is impossible ( 11. Ax . ) The angles ...
... parallel to CD ( 27. 1. ) ; but E AB is also parallel to CD ; therefore two straight lines G are drawn through the same point G , parallel to CD , and K yet not coinciding with one an- other , which is impossible ( 11. Ax . ) The angles ...
Σελίδα 41
... 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 straight line through a given point parallel to a given straight line . A Let A be the given point , and BC the ...
... 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 straight line through a given point parallel to a given straight line . A Let A be the given point , and BC the ...
Σελίδα 42
... parallel to CE , and BD falls upon them , the exterior angle ECD is 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 ...
... parallel to CE , and BD falls upon them , the exterior angle ECD is 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 ...
Σελίδα 43
... 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 meets them ...
... 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 meets them ...
Σελίδα 44
... parallels , are equal to one another . ( SEE THE 20 AND 3d FIGURES . ) Let the parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If ...
... parallels , are equal to one another . ( SEE THE 20 AND 3d FIGURES . ) Let the parallelograms ABCD , EBCF be upon the same base BC , and between the same parallels AF , BC ; the parallelogram ABCD is equal to the parallelogram EBCF . If ...
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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