The Elements of Solid GeometryLeach, Shewell & Sanborn, 1893 - 95 σελίδες |
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Σελίδα 35
... ABC : DEF :: H2 : h2 ... ( 117 ) ; A'B'C ' : D'E'F ' :: H2 : h2 ; ABC : DEF :: A'B'C ' : D'E'F ' . and , Hence , But , ABC A'B'C ' ( hypothesis ) ; hence DEF D'E'F ' . Q. E. D. PROPOSITION XXI . 119. THEOREM . Triangular pyramids having ...
... ABC : DEF :: H2 : h2 ... ( 117 ) ; A'B'C ' : D'E'F ' :: H2 : h2 ; ABC : DEF :: A'B'C ' : D'E'F ' . and , Hence , But , ABC A'B'C ' ( hypothesis ) ; hence DEF D'E'F ' . Q. E. D. PROPOSITION XXI . 119. THEOREM . Triangular pyramids having ...
Σελίδα 36
... def and ghk in pyramid o , and d'e'f ' and g'h'k ' in pyramid o ' . At pyramid o , construct the prisms abc - d , def - g , and ghk - o ; and in pyramid o ' construct the prisms d'e'f ' - a ' and g'h'k ' - d ' . ( a ) . It is evident ...
... def and ghk in pyramid o , and d'e'f ' and g'h'k ' in pyramid o ' . At pyramid o , construct the prisms abc - d , def - g , and ghk - o ; and in pyramid o ' construct the prisms d'e'f ' - a ' and g'h'k ' - d ' . ( a ) . It is evident ...
Σελίδα 62
... respect to two sides and their included angle . IV . If they are mutually equal with respect to two angles and their common side . AAD CASE I. Let the spherical triangles ABC and DEF , 62 THE ELEMENTS OF SOLID GEOMETRY .
... respect to two sides and their included angle . IV . If they are mutually equal with respect to two angles and their common side . AAD CASE I. Let the spherical triangles ABC and DEF , 62 THE ELEMENTS OF SOLID GEOMETRY .
Σελίδα 63
... ABC and DEF ( 187 and 189 ) . Now , O and O ' have three face angles of the one equal to three face angles of the other , each to each ( 188 ) . Hence O and O ' are mutually equal in all their parts ( 46 ) . But , if O and O ' are ...
... ABC and DEF ( 187 and 189 ) . Now , O and O ' have three face angles of the one equal to three face angles of the other , each to each ( 188 ) . Hence O and O ' are mutually equal in all their parts ( 46 ) . But , if O and O ' are ...
Σελίδα 64
... ABC and DEF are mutu- ally equal with respect to all their parts ( 188 ) . Q. E. D. CASE IV . See diagram , Case II . Let the spherical triangles ABC and DEF be mutually equal with respect to two angles and their common side ; then ABC ...
... ABC and DEF are mutu- ally equal with respect to all their parts ( 188 ) . Q. E. D. CASE IV . See diagram , Case II . Let the spherical triangles ABC and DEF be mutually equal with respect to two angles and their common side ; then ABC ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
ABC and DEF ABC-B altitude are equal axis base and altitude bases are equal bisecting centre circle circumference coincide common altitude common vertex conical surface COROLLARY cube cuboid DEFINITIONS diameter dicular diedral angle EDC-O equal with respect equivalent faces is called feet Find the volume frustum Hence inscribed prism intersection lateral edges lateral faces lateral surface Let the line line BA lune MN and PQ mutually equal O-ABCD oblique parallelopiped parallel planes parallelogram pass perimeter perpen perpendicular to MN plane angle plane MN plane PQ polar triangle polyedral angle prisms whose bases radii radius regular polyedrons regular polygon right angles right circular cone right prism right section SCHOLIUM sides slant height sphere spherical angle spherical excess spherical polygon spherical triangle straight line tetraedron THEOREM triangles ABC triangular prism triangular pyramids triedral
Δημοφιλή αποσπάσματα
Σελίδα 48 - Assuming that the areas of two triangles which have 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 46 - Similar cylinders are to each other as the cubes of their altitudes, or as the cubes of the diameters of their bases.
Σελίδα 4 - If a straight line is perpendicular to each of two other straight lines at their point of intersection, it is perpendicular to the plane of the two lines.
Σελίδα 49 - A sphere is a solid bounded by a curved surface, every point of which is equally distant from a point within called the center.
Σελίδα 94 - Two triangles are equal if two sides and the included angle of the one are equal respectively to two sides and the included angle of the other (sas = sas). Hyp. In A ABC and A'B'C', AB = A'B', BC = B'C', and Z B = Z B'.
Σελίδα 46 - The lateral areas, or the total -areas, of two similar cones of revolution are to each other as the squares of their altitudes...
Σελίδα 6 - Theorem: If a straight line is perpendicular to one of two parallel planes, it is perpendicular, also, to the other plane.
Σελίδα 9 - ... meeting the plane at unequal distances from the foot of the perpendicular the more remote is the greater.
Σελίδα 56 - A spherical angle is measured by the arc of a great circle described from its vertex as a pole, and included between its sides, produced if necessary.