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 17
... distances , therefrom , be measured , on the sphere's surface , by arches of great circles passing through those points and the pole ; or by straight lines , joining those points and the pole and conversely , if a point on a sphere's ...
... distances , therefrom , be measured , on the sphere's surface , by arches of great circles passing through those points and the pole ; or by straight lines , joining those points and the pole and conversely , if a point on a sphere's ...
Σελίδα 19
... Distance is the straight line which joins them : and their Spherical Distance is the arch of a great circle which joins them : Also , the distance of the pole of any circle , in a sphere , from any point in the circumference of the ...
... Distance is the straight line which joins them : and their Spherical Distance is the arch of a great circle which joins them : Also , the distance of the pole of any circle , in a sphere , from any point in the circumference of the ...
Σελίδα 20
... Distance of that circle . ( 35. ) DEF . The fourth part of the circumference of a great circle , in a sphere , is called a Quadrant . PROP . VIII . ( 36. ) Theorem . The polar distance of a great circle , in a sphere , is a quadrant ...
... Distance of that circle . ( 35. ) DEF . The fourth part of the circumference of a great circle , in a sphere , is called a Quadrant . PROP . VIII . ( 36. ) Theorem . The polar distance of a great circle , in a sphere , is a quadrant ...
Σελίδα 21
... distance of G R H B L K p a quadrant , from any two points , A and B , in the circum- ference of the great circle ... distances of equal circles , in a sphere , are equal to one another : And circles in a sphere , which have equal polar ...
... distance of G R H B L K p a quadrant , from any two points , A and B , in the circum- ference of the great circle ... distances of equal circles , in a sphere , are equal to one another : And circles in a sphere , which have equal polar ...
Σελίδα 22
... distances are equal , because ( Art . 36. ) each of them is a quadrant . But , let EH and Al be two lesser circles in ... distance of AI : For , let EH and AI be any diameters of the circles EH and AI : and let EPH and AQI be arches of ...
... distances are equal , because ( Art . 36. ) each of them is a quadrant . But , let EH and Al be two lesser circles in ... distance of AI : For , let EH and AI be any diameters of the circles EH and AI : and let EPH and AQI be arches of ...
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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.