A Treatise on Spherics: Comprising the Elements of Spherical Geometry, and of Plane and Spherical Trigonometry, Together with a Series of Trigonometrical TablesJ. Mawman, 1816 - 294 σελίδες |
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Σελίδα x
... shewn the mode , or at least the possibility , of actually cal- culating such values , to any required degree of exactness . These latter remarks apply , more especially , to the doctrine of Plane Trigonometry , which is here treated of ...
... shewn the mode , or at least the possibility , of actually cal- culating such values , to any required degree of exactness . These latter remarks apply , more especially , to the doctrine of Plane Trigonometry , which is here treated of ...
Σελίδα 5
... shewn to be equal to GE , or GF . Therefore ( E. Def . 15. 1. ) the figure EFH is a circle . The proposition may also be proved , by shewing that any two straight lines in EFH , drawn through G , and terminated by the sphere's surface ...
... shewn to be equal to GE , or GF . Therefore ( E. Def . 15. 1. ) the figure EFH is a circle . The proposition may also be proved , by shewing that any two straight lines in EFH , drawn through G , and terminated by the sphere's surface ...
Σελίδα 6
... shewn to be equal , by applying the one to the other so that their centers shall coincide : for then the one figure must wholly coincide with the other . In the same manner , also , it may be shewn , that of two circles that which has ...
... shewn to be equal , by applying the one to the other so that their centers shall coincide : for then the one figure must wholly coincide with the other . In the same manner , also , it may be shewn , that of two circles that which has ...
Σελίδα 8
... shewn , conversely , that the greater of two circles , in a sphere , is nearer to the sphere's center than the less , and that equal circles , which do not pass through the sphere's center , are equally distant from it . ( 12. ) COR . 2 ...
... shewn , conversely , that the greater of two circles , in a sphere , is nearer to the sphere's center than the less , and that equal circles , which do not pass through the sphere's center , are equally distant from it . ( 12. ) COR . 2 ...
Σελίδα 14
... shewn to pass through CG , which line produced is ( Art . 20. ) the axis of EFH : wherefore ( Art . 21. ) it passes through the poles of EFH . Conversely , let the great circle PEpH pass through the two poles P and p of EFH , and let ...
... shewn to pass through CG , which line produced is ( Art . 20. ) the axis of EFH : wherefore ( Art . 21. ) it passes through the poles of EFH . Conversely , let the great circle PEpH pass through the two poles P and p of EFH , and let ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
angle opposite base bisect circle EFH circumference co-tangent common section cosine describe a circle describe Art diameter drawn equal and parallel equal arches equal circles equal spheres equal to FE equations Euclid's Elements Find Art fore four right angles given angle given arch given circle given great circle given point given sphere given triangle greater hypotenuse Introd join Art less measure meet oblique angles opposite angle parallel circles perpendicular plane triangle polar distance polar triangle pole Problem PROP proposition quadrantal triangle radius rical triangle right angles right-angled spherical triangle SCHOLIUM semi-circumference shewn side BC sin S sin sine sphe sphere's center sphere's surface spherical angle spherical distance Spherical Geometry spherical polygon spherical tri Spherical Trigonometry straight line tangent Theorem three angles three sides touch the circle triangle ABC trigonometrical functions wherefore
Δημοφιλή αποσπάσματα
Σελίδα 53 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 46 - BC shall be equal to the base EF ; and the triangle ABC to the triangle DEF ; and the other angles, to which the equal sides are opposite, shall be equal, each to each, viz.
Σελίδα iii - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Σελίδα 43 - Theorem. If two spherical triangles on the same sphere, or on equal spheres, are equilateral with respect to each other, they are also equiangular with respect to each other.
Σελίδα 53 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 53 - BC common to the two triangles, which is adjacent to their equal angles ; therefore their other sides shall be equal, each to each, and the third angle of the one to the third angle of the other, (26.
Σελίδα iii - A diameter of a circle is a straight line drawn through the center and terminated both ways by the circumference, as AC in Fig.
Σελίδα 132 - If two triangles have two sides and the included angle in the one equal to two sides and the included angle in the other, each to each, the two triangles will be equal.
Σελίδα 38 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Σελίδα 50 - If two angles of a triangle be equal to one another, the sides also which subtend the equal angles shall be equal to one another.