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 Trigonometry |
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Page 18
... Spherical Trigonometry John Playfair. A B D E C N. B. When several angles are at one point B , any one of them ' is expressed by three letters , of which the letter that is at the ver- ' tex of the angle , that is , at the point in which ...
... Spherical Trigonometry John Playfair. A B D E C N. B. When several angles are at one point B , any one of them ' is expressed by three letters , of which the letter that is at the ver- ' tex of the angle , that is , at the point in which ...
Page 24
... Spherical Trigonometry John Playfair. posite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D ...
... Spherical Trigonometry John Playfair. posite , shall be equal , each to each , viz . the angle ABC to the angle DEF , and the angle ACB to DFE . For , if the triangle ABC be applied to the triangle DEF , so that the point A may be on D ...
Page 25
... Spherical Trigonometry John Playfair ! A remainder CG ; and FC was proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the ...
... Spherical Trigonometry John Playfair ! A remainder CG ; and FC was proved to be equal to GB , therefore the two sides BF , FC are equal to the two CG , GB , each to each ; but the angle BFC is equal to the angle CGB ; wherefore the ...
Page 26
... Spherical Trigonometry John Playfair. B , cannot be equal to one another . Join CD , and if possible let CB be equal ... angle ACD is equal ( 5. 1. ) to the angle ADC : But the angle ACD is greater than the angle BCD ; there- C D ...
... Spherical Trigonometry John Playfair. B , cannot be equal to one another . Join CD , and if possible let CB be equal ... angle ACD is equal ( 5. 1. ) to the angle ADC : But the angle ACD is greater than the angle BCD ; there- C D ...
Page 27
... Spherical Trigonometry John Playfair. B A DG C E F to DF ; and also the base BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and ...
... Spherical Trigonometry John Playfair. B A DG C E F to DF ; and also the base BC equal to the base EF . The angle BAC is equal to the angle EDF . For , if the triangle ABC be applied to the triangle DEF , so that the point B be on E , and ...
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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 definition 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 MDCCCXX 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