Elementary GeometryJ.B. Lippincott Company, 1893 |
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Page 271
... spherical triangle is a spherical polygon of three sides . It is called right angled , isosceles , or equilat- eral , in the same cases as a plane triangle . 45. In consequence of the relation established between polyedral angles and ...
... spherical triangle is a spherical polygon of three sides . It is called right angled , isosceles , or equilat- eral , in the same cases as a plane triangle . 45. In consequence of the relation established between polyedral angles and ...
Page 272
... spherical triangles are symmetrical if all the parts of one are respectively ... triangle would have to be turned over , and the two convex surfaces would ... spherical triangle and AB = AC , then , in its symmetrical triangle , we have A ...
... spherical triangles are symmetrical if all the parts of one are respectively ... triangle would have to be turned over , and the two convex surfaces would ... spherical triangle and AB = AC , then , in its symmetrical triangle , we have A ...
Page 277
... will no longer be equal , but will be proportional to the radii of the sphere ; the two triangles will then be similar , as in the case of plane triangles . EXERCISES . 1. Theorem . In an isosceles spherical triangle 24 BOOK VIII . 277.
... will no longer be equal , but will be proportional to the radii of the sphere ; the two triangles will then be similar , as in the case of plane triangles . EXERCISES . 1. Theorem . In an isosceles spherical triangle 24 BOOK VIII . 277.
Page 278
... spherical triangle to the middle point of the base is perpendicular to the base , and bisects the vertical angle . 3. Theorem . - If two angles of a spherical triangle are equal , the triangle is isosceles . PROPOSITION XVI . - THEOREM ...
... spherical triangle to the middle point of the base is perpendicular to the base , and bisects the vertical angle . 3. Theorem . - If two angles of a spherical triangle are equal , the triangle is isosceles . PROPOSITION XVI . - THEOREM ...
Page 279
... spherical triangle is greater than two , and less than six , right angles . For , denoting the angles of a spherical tri- angle by A , B , C , and the sides respectively opposite to them in its polar triangle by a ' , b ' , c ' , we ...
... spherical triangle is greater than two , and less than six , right angles . For , denoting the angles of a spherical tri- angle by A , B , C , and the sides respectively opposite to them in its polar triangle by a ' , b ' , c ' , we ...
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Common terms and phrases
ABCD adjacent angles altitude angle BAC angles are equal apothem bisects centre chord coincide common cone construct convex Corollary cylinder Definition diagonal diameter dicular diedral angle distance divided draw equal circles equally distant equilateral equivalent Exercise find the locus frustum given circle given line given point given straight line greater Hence hypotenuse included angle inscribed angle intercepted arcs isosceles triangle lateral area lateral edges mean proportional middle point number of sides parallel lines parallelogram parallelopiped pass a plane pendicular perimeter perpen perpendicular plane MN plane passed polyedral angle Proposition VI Proposition VII quadrilateral radii radius ratio rectangle regular inscribed regular polygon respectively equal right angles right triangle Scholium secant secant line segment similar slant height sphere spherical polygon spherical triangle square surface tangent tetraedron Theorem triangle ABC triangles are equal triangular prism triedral upper base vertex volume
Popular passages
Page 127 - The area of a rectangle is equal to the product of its base and altitude.
Page 196 - If a straight line is perpendicular to each of two straight lines at their point of intersection, it is perpendicular to the plane of those lines.
Page 131 - Two triangles having an angle of the one equal to an angle of the other are to each other as the products of the sides including the equal angles.
Page 245 - A truncated triangular prism is equivalent to the sum of three pyramids whose common base is the base of the prism, and whose vertices are the three vertices of the inclined section.
Page 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Page 111 - The square of the length of the hypotenuse of a right triangle is equal to the sum of the squares of the lengths of the other two sides.
Page 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Page 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Page 34 - The sum of the three angles of any triangle is equal to two right angles.