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 22
... Spherical Trigonometry John Playfair. PROPOSITION I. PROBLEM . To describe an equilateral triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From ...
... Spherical Trigonometry John Playfair. PROPOSITION I. PROBLEM . To describe an equilateral triangle upon a given finite straight line Let AB be the given straight line ; it is required to describe an equilateral triangle upon it . From ...
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 ... triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon ...
... Spherical Trigonometry John Playfair ! A remainder CG ; and FC was proved to be equal to GB , therefore the two ... triangle ABC : And it has also been proved that the angle FBC is equal to the angle GCB , which are the angles upon ...
Page 26
... Spherical Trigonometry John Playfair. B , cannot be equal to one another . Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of each of the triangles is without the other trian- gle , because AC is ...
... Spherical Trigonometry John Playfair. B , cannot be equal to one another . Join CD , and if possible let CB be equal to DB ; then , in the case in which the vertex of each of the triangles is without the other trian- gle , because AC is ...
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