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 páginas |
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Página viii
... circumferences of which are in its surface : and all this he can do , by a series of common and easy operations , per- formed by a rule and compass ; the whole solution of the problem , mainly depending upon this plain theorem , that if ...
... circumferences of which are in its surface : and all this he can do , by a series of common and easy operations , per- formed by a rule and compass ; the whole solution of the problem , mainly depending upon this plain theorem , that if ...
Página 10
... circumference of a given circle , there can only pass one great circle at right angles to the given circle . ( 19. ) COR . 4. Two great circles of a sphere can- not ( Art . 7. ) be parallel : but there may be an indefinite number of ...
... circumference of a given circle , there can only pass one great circle at right angles to the given circle . ( 19. ) COR . 4. Two great circles of a sphere can- not ( Art . 7. ) be parallel : but there may be an indefinite number of ...
Página 11
... circumference of a great circle pass through one of the poles of a given circle in a sphere , passes also through the other pole of that circle . it For the plane of the great circle passes through the sphere's center ; if , therefore ...
... circumference of a great circle pass through one of the poles of a given circle in a sphere , passes also through the other pole of that circle . it For the plane of the great circle passes through the sphere's center ; if , therefore ...
Página 12
... circumference of the other , the poles of the latter are also in the circumference of the former , and the two circles are perpendicular to one another . First , if the two great circles cut each other at right angles , a diameter in ...
... circumference of the other , the poles of the latter are also in the circumference of the former , and the two circles are perpendicular to one another . First , if the two great circles cut each other at right angles , a diameter in ...
Página 13
... circumference of the other , the axis ( Art . 20. ) of the one lies in the plane of the other ; and therefore ( Art ... circumference . PROP . V. ( 28. ) Theorem . If a great circle pass through the diameter of a lesser circle , in a ...
... circumference of the other , the axis ( Art . 20. ) of the one lies in the plane of the other ; and therefore ( Art ... circumference . PROP . V. ( 28. ) Theorem . If a great circle pass through the diameter of a lesser circle , in a ...
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Términos y frases comunes
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
Pasajes populares
Página 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...
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 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.
Página 38 - THEOREM. The sum of the sides of a spherical polygon is less than the circumference of a great circle.
Página 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.