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 27
... touching any two circular arches , on a sphere's surface , which include a spherical angle , the one straight line touching the one arch , and the other the other , in their point of concourse , * The reclination of two such arches from ...
... touching any two circular arches , on a sphere's surface , which include a spherical angle , the one straight line touching the one arch , and the other the other , in their point of concourse , * The reclination of two such arches from ...
Página 28
... touching PF in P , and Py a straight line that touches PH in P , the plane rectilineal angle x Py is equal to the spherical angle FPH . ( 42. ) COR . 1. If two arches of circles , in a sphere's surface , meet together , they make with ...
... touching PF in P , and Py a straight line that touches PH in P , the plane rectilineal angle x Py is equal to the spherical angle FPH . ( 42. ) COR . 1. If two arches of circles , in a sphere's surface , meet together , they make with ...
Página 29
... touch any number of great circles , of a sphere , in their common point of intersection , are in the same plane . For ( E. 18. 3. ) the tangent straight lines are all per- pendicular to that diameter of the sphere , which is the common ...
... touch any number of great circles , of a sphere , in their common point of intersection , are in the same plane . For ( E. 18. 3. ) the tangent straight lines are all per- pendicular to that diameter of the sphere , which is the common ...
Página 32
... touching EFH , in F , is parallel to EG : but ( E. Def . 4. 11. ) EG is perpendicular to the plane PFp ; therefore ( E. 8. 11. ) the tangent of EFH , at F , is per- pendicular to the plane PFp , and , therefore , it is perpen- dicular ...
... touching EFH , in F , is parallel to EG : but ( E. Def . 4. 11. ) EG is perpendicular to the plane PFp ; therefore ( E. 8. 11. ) the tangent of EFH , at F , is per- pendicular to the plane PFp , and , therefore , it is perpen- dicular ...
Página 34
... touching PFp in P , and Py , touching PHp in P : and from any point G , in Pp , let there be drawn GF , in the plane PFp , and GH in the plane PHp , each of them perpen- dicular to Pp : so that ( E. Def . 6. 11. ) the angle FGH is the ...
... touching PFp in P , and Py , touching PHp in P : and from any point G , in Pp , let there be drawn GF , in the plane PFp , and GH in the plane PHp , each of them perpen- dicular to Pp : so that ( E. Def . 6. 11. ) the angle FGH is the ...
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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.