Elementary GeometryJ.B. Lippincott Company, 1893 |
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Σελίδα 8
... SPHERE . SPHERICAL TRIANGLES . SPHERICAL POLY- PAGE 195 220 224 254 GONS EXERCISES ON BOOK VIII . 257 287 BOOK IX . MEASUREMENT OF THE THREE ROUND BODIES 290 EXERCISES ON BOOK IX .. • · 308 MISCELLANEOUS EXERCISES ON SOLID GEOMETRY 809 ...
... SPHERE . SPHERICAL TRIANGLES . SPHERICAL POLY- PAGE 195 220 224 254 GONS EXERCISES ON BOOK VIII . 257 287 BOOK IX . MEASUREMENT OF THE THREE ROUND BODIES 290 EXERCISES ON BOOK IX .. • · 308 MISCELLANEOUS EXERCISES ON SOLID GEOMETRY 809 ...
Σελίδα 264
... sphere , the lines joining points on the perimeter of the section with the centre of the sphere are radii of the sphere , and are therefore all equal . Consequently it is a circle with its centre at O. 2d . If the plane does not pass ...
... sphere , the lines joining points on the perimeter of the section with the centre of the sphere are radii of the sphere , and are therefore all equal . Consequently it is a circle with its centre at O. 2d . If the plane does not pass ...
Σελίδα 265
... sphere and is a diame- ter of each circle . 27. COROLLARY V. An arc of a great circle may be drawn through any two given points of the surface of the sphere , and , unless the points are the opposite extremities E of a diameter , only ...
... sphere and is a diame- ter of each circle . 27. COROLLARY V. An arc of a great circle may be drawn through any two given points of the surface of the sphere , and , unless the points are the opposite extremities E of a diameter , only ...
Σελίδα 267
William Chauvenet. In connection with the sphere , by a quadrant is usually to be understood a quadrant of a great circle . 32. COROLLARY III . If a point on the surface of a sphere is at a quadrant's distance from each of two given ...
William Chauvenet. In connection with the sphere , by a quadrant is usually to be understood a quadrant of a great circle . 32. COROLLARY III . If a point on the surface of a sphere is at a quadrant's distance from each of two given ...
Σελίδα 269
... spheres , and the point A will describe the line of intersection of their surfaces . Moreover , since the line AC ... sphere . TA and T'A lie in the planes of their arcs , and are perpendicular to the radius OA drawn to their point of ...
... spheres , and the point A will describe the line of intersection of their surfaces . Moreover , since the line AC ... sphere . TA and T'A lie in the planes of their arcs , and are perpendicular to the radius OA drawn to their point of ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
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
Δημοφιλή αποσπάσματα
Σελίδα 127 - The area of a rectangle is equal to the product of its base and altitude.
Σελίδα 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.
Σελίδα 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.
Σελίδα 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.
Σελίδα 278 - A lune is to the, surface of the sphere as the angle of the lune is to four right angles. Let...
Σελίδα 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.
Σελίδα 48 - The three perpendiculars from the vertices of a triangle to the opposite sides meet in the same point.
Σελίδα 57 - A tangent to a circle is perpendicular to the radius drawn to the point of contact.
Σελίδα 34 - The sum of the three angles of any triangle is equal to two right angles.