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
... equal angles of equiangular triangles , the first , it is soon discovered , has no existence at all in Spherics ... circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel circles ...
... equal angles of equiangular triangles , the first , it is soon discovered , has no existence at all in Spherics ... circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel circles ...
Σελίδα ii
... equal angles of equiangular triangles , the first , it is soon discovered , has no existence at all in Spherics ... circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel circles ...
... equal angles of equiangular triangles , the first , it is soon discovered , has no existence at all in Spherics ... circles whatever of the sphere , be equal ; and , if not , whether there is not one par- ticular pair of parallel circles ...
Σελίδα viii
... circles be described about triangles , which have the sides of the one severally equal to the sides of the other , the diameters of the circles are equal to one another . In the following pages , therefore , regard has been had to ...
... circles be described about triangles , which have the sides of the one severally equal to the sides of the other , the diameters of the circles are equal to one another . In the following pages , therefore , regard has been had to ...
Σελίδα 6
... equal to one another . ( 7. ) COR . 1. If a sphere be cut by any two planes , passing through its center , the two ... circles , of which the diameters are equal , may be shewn to be equal , by applying the one to the other so that their ...
... equal to one another . ( 7. ) COR . 1. If a sphere be cut by any two planes , passing through its center , the two ... circles , of which the diameters are equal , may be shewn to be equal , by applying the one to the other so that their ...
Σελίδα 7
... Circles in a sphere are said to be equally distant from the sphere's center , when the per- pendiculars drawn to their planes from the sphere's center are equal : and that circle is said to be the farther distant , upon the plane of ...
... Circles in a sphere are said to be equally distant from the sphere's center , when the per- pendiculars drawn to their planes from the sphere's center are equal : and that circle is said to be the farther distant , upon the plane of ...
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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.