The Elements of Solid GeometryLeach, Shewell & Sanborn, 1893 - 95 σελίδες |
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Αποτελέσματα 1 - 5 από τα 20.
Σελίδα 6
... triangle ABC is equal to the triangle A'B'C ' ( 357 ) , in which tri- angles , any angle ABC is equal to the corresponding angle A'B'C ' . And these angles have their sides parallel , each to each , and lying in different planes . · 20 ...
... triangle ABC is equal to the triangle A'B'C ' ( 357 ) , in which tri- angles , any angle ABC is equal to the corresponding angle A'B'C ' . And these angles have their sides parallel , each to each , and lying in different planes . · 20 ...
Σελίδα 13
... ABC , let AOC be the greatest ; then will AOC AOB + BOC . Draw OD making the angle AOD equal to the angle AOB . Take DO , AO , and BO equal to each other . Draw AD pro- duced to meet OC in some point C. Draw AB and BC . The triangles ...
... ABC , let AOC be the greatest ; then will AOC AOB + BOC . Draw OD making the angle AOD equal to the angle AOB . Take DO , AO , and BO equal to each other . Draw AD pro- duced to meet OC in some point C. Draw AB and BC . The triangles ...
Σελίδα 15
... angle aoc equals the triangle a'o'c ' ( 355 ) , equals a'c ' . and hence ac Now , the triangles abc and a'b'c ' , being mutually equilat- eral , are equal , and hence the angle abc equals the angle a'b'c . But abc and a'b'e are the ...
... angle aoc equals the triangle a'o'c ' ( 355 ) , equals a'c ' . and hence ac Now , the triangles abc and a'b'c ' , being mutually equilat- eral , are equal , and hence the angle abc equals the angle a'b'c . But abc and a'b'e are the ...
Σελίδα 24
... ABC - B ' and ADC - D ' , thus formed , be equivalent . Any right section EFGH is a parallelogram ( 66 , b ) , and EG , drawn from vertex E to vertex G , is a diagonal . Hence the triangle EFG equals the triangle EHG . ( 359. ) The prisms ...
... ABC - B ' and ADC - D ' , thus formed , be equivalent . Any right section EFGH is a parallelogram ( 66 , b ) , and EG , drawn from vertex E to vertex G , is a diagonal . Hence the triangle EFG equals the triangle EHG . ( 359. ) The prisms ...
Σελίδα 34
... angle A'B'C ' equals ABC ... ( 19 ) . And in like manner we can prove that the section and the base have corresponding angles equal , each to each , throughout . Now , triangle and triangle OAB is similar to OA'B ' . ( 362 ) ; OBC is ...
... angle A'B'C ' equals ABC ... ( 19 ) . And in like manner we can prove that the section and the base have corresponding angles equal , each to each , throughout . Now , triangle and triangle OAB is similar to OA'B ' . ( 362 ) ; OBC is ...
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.