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
... Plane and Spherical Trigonometry John Playfair. DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis ...
... Plane and Spherical Trigonometry John Playfair. DEF , and the other angles to the other angles , each to each , to which the equal sides are opposite ; therefore the angle GCB is equal to the angle DFE but DFE is , by the hypothesis ...
Σελίδα 39
... Plane and Spherical Trigonometry John Playfair. A E B G D its exterior angle AEF is greater ( 16. 1. ) than the interior and oppo site angle EFG ; but it is also equal to it , which is impossible therefore , AB and CD being produced , do ...
... Plane and Spherical Trigonometry John Playfair. A E B G D its exterior angle AEF is greater ( 16. 1. ) than the interior and oppo site angle EFG ; but it is also equal to it , which is impossible therefore , AB and CD being produced , do ...
Σελίδα 42
... Plane and Spherical Trigonometry John Playfair. 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 ...
... Plane and Spherical Trigonometry John Playfair. 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 ...
Σελίδα 44
... Plane and Spherical Trigonometry John Playfair. the third angle of the one to the third angle of the other ( 26. 1. ) , viz . the side AB to the side CD , and AC to BD , and the angle BAC equal to the angle BDC . And because the angle ...
... Plane and Spherical Trigonometry John Playfair. the third angle of the one to the third angle of the other ( 26. 1. ) , viz . the side AB to the side CD , and AC to BD , and the angle BAC equal to the angle BDC . And because the angle ...
Σελίδα 47
... Plane and Spherical Trigonometry John Playfair. PROP . XL . THEOR . Equal triangles on the same side of bases , which are equal and in the same straight line , are between the same parallels . Let the equal triangles ABC , DEF be upon ...
... Plane and Spherical Trigonometry John Playfair. PROP . XL . THEOR . Equal triangles on the same side of bases , which are equal and in the same straight line , are between the same parallels . Let the equal triangles ABC , DEF be upon ...
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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