Elements of Plane and Solid GeometryGinn, Heath, 1877 - 398 σελίδες |
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Σελίδα vi
... contained in [ 4 ] , page 88. If x increase and approach the altitude a as a limit , the area of the rec- tangle increases and approaches the area of the rectangle ab as a limit ; if , however , a decrease and approach zero as a limit ...
... contained in [ 4 ] , page 88. If x increase and approach the altitude a as a limit , the area of the rec- tangle increases and approaches the area of the rectangle ab as a limit ; if , however , a decrease and approach zero as a limit ...
Σελίδα 86
... contained in a ; or , what part a is of b . α b . I. If b be contained an exact number of times in a their ratio is a whole number . Ifb be not contained an exact number of times in a , but if there be a common measure which is contained ...
... contained in a ; or , what part a is of b . α b . I. If b be contained an exact number of times in a their ratio is a whole number . Ifb be not contained an exact number of times in a , but if there be a common measure which is contained ...
Σελίδα 87
... contained m ' times in a with a remainder 1 less than part of b , then n2 of the ratio , correct within b m ' n 1 n2 is a nearer approximate value By continuing this process , a series of variable values , 172 m ' m ' n n2 39 etc ...
... contained m ' times in a with a remainder 1 less than part of b , then n2 of the ratio , correct within b m ' n 1 n2 is a nearer approximate value By continuing this process , a series of variable values , 172 m ' m ' n n2 39 etc ...
Σελίδα 90
... contain one or more of the factors v , v ' , v ' , and hence have zero for a limit . [ 3 ] .. lim . ( x y z ) = lim ... contained in Proposition I .; and it will be left as an exercise for the student to determine in each case what ...
... contain one or more of the factors v , v ' , v ' , and hence have zero for a limit . [ 3 ] .. lim . ( x y z ) = lim ... contained in Proposition I .; and it will be left as an exercise for the student to determine in each case what ...
Σελίδα 91
... contained in A B three times , and in AC five times . Then arc AB = 3 • arc A C 5 At the several points of division on A B and A C draw radii . These radii will divide AOC into five equal parts , of which AOB will contain three , $ 180 ...
... contained in A B three times , and in AC five times . Then arc AB = 3 • arc A C 5 At the several points of division on A B and A C draw radii . These radii will divide AOC into five equal parts , of which AOB will contain three , $ 180 ...
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
A B C D AABC ABCD altitude apothem arcs A B axis base and altitude centre centre of symmetry chord circumference circumscribed coincide conical surface COROLLARY cylinder denote diagonals diameter dihedral angle distance divided draw equal respectively equally distant equilateral equivalent frustum given point Hence homologous sides hypotenuse intersection isosceles lateral area lateral edges lateral faces Let A B Let ABC line A B measured by arc middle point number of sides opposite parallel lines parallelogram parallelopiped perimeter perpendicular plane MN polyhedral angle prove Q. E. D. PROPOSITION radii ratio rect rectangles regular inscribed regular polygon right angles right section SCHOLIUM similar polygons slant height sphere spherical angle spherical polygon spherical triangle straight line drawn surface tangent tetrahedron THEOREM trihedral upper base vertex vertices volume
Δημοφιλή αποσπάσματα
Σελίδα 188 - 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 347 - A sphere is a solid bounded by a surface all points of which are equally distant from a point within called the centre.
Σελίδα 134 - In a series of equal ratios, the sum of the antecedents is to the sum of the consequents as any antecedent is to its consequent.
Σελίδα 201 - To construct a parallelogram equivalent to a given square, and having the sum of its base and altitude equal to a given line.
Σελίδα 221 - The area of a regular inscribed hexagon is a mean proportional between the areas of the inscribed and circumscribed equilateral triangles.
Σελίδα 217 - The area of a regular polygon is equal to onehalf the product of its apothem and perimeter.
Σελίδα 44 - Two triangles are equal if the three sides of the one are equal, respectively, to the three sides of the other. In the triangles ABC and A'B'C', let AB be equal to A'B', AC to A'C', BC to B'C'. To prove that A ABC = A A'B'C'.
Σελίδα 186 - In any triangle, the square of the side opposite an acute angle is equal to the sum of the squares of the other two sides diminished by twice the product of one of those sides and the projection of the other upon that side.
Σελίδα 346 - A frustum of any pyramid is equivalent to the sum of three pyramids whose common altitude is the altitude of the frustum, and whose bases are the lower base, the upper base, and a mean proportional between the bases, of the frustum. For, let ABCDE-F be a frustum of any pyramid S-ABCDE. Let S'-A'B'C' be a triangular pyramid, having the same altitude as the pyramid S-ABCDE, and a base A'B'C' equivalent to the base ABCDE, and in the same plane with it.
Σελίδα 95 - BAC, inscribed in a segment greater than a semicircle, is an acute angle ; for it is measured by half of the arc BOC, less than a semicircumference.