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 172
... cosine , co - tangent , and co - secant of an arch , are , respectively , the sine , the tangent , and the secant of its complement . Thus , if AP be any arch , less than a quadrant , of the circle ABCD , having K for its center , let ...
... cosine , co - tangent , and co - secant of an arch , are , respectively , the sine , the tangent , and the secant of its complement . Thus , if AP be any arch , less than a quadrant , of the circle ABCD , having K for its center , let ...
Σελίδα 173
... cosine of AP , and of CBP . AG is the tangent , and KG the secant of AB , and of ECBA . CL is the tangent , and KL the secant , of CBP . BI is the co - tangent , and KI the co - secant , of AP , and of CBP . EM is the sine , and EN the ...
... cosine of AP , and of CBP . AG is the tangent , and KG the secant of AB , and of ECBA . CL is the tangent , and KL the secant , of CBP . BI is the co - tangent , and KI the co - secant , of AP , and of CBP . EM is the sine , and EN the ...
Σελίδα 174
... cosine , tangent and secant of the supplement of that arch . ( 15. ) COR . 2. That part of a diameter , passing through the extremity of an arch , which lies between its sine , and the center of the circle is ( E. 34. 1. ) equal to the ...
... cosine , tangent and secant of the supplement of that arch . ( 15. ) COR . 2. That part of a diameter , passing through the extremity of an arch , which lies between its sine , and the center of the circle is ( E. 34. 1. ) equal to the ...
Σελίδα 175
... cosine , tangent , co- tangent , secant and co - secant may be found , of an arch , of the same number of degrees , in a circle of any other given radius ( 15. 16. 17 ) . ( 19. ) COR . 6. It is manifest , PLANE TRIGONOMETRY . 175.
... cosine , tangent , co- tangent , secant and co - secant may be found , of an arch , of the same number of degrees , in a circle of any other given radius ( 15. 16. 17 ) . ( 19. ) COR . 6. It is manifest , PLANE TRIGONOMETRY . 175.
Σελίδα 176
... cosine , is the radius of the circle ; but that a sine , or a cosine , may be found , that is less than any given finite straight line : and that the values of a tangent , or a co - tangent , a secant , or co- secant , may be either ...
... cosine , is the radius of the circle ; but that a sine , or a cosine , may be found , that is less than any given finite straight line : and that the values of a tangent , or a co - tangent , a secant , or co- secant , may be either ...
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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.