Elements of Geometry |
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Σελίδα
In this edition I have endeavored to present a more rigorous , but not less simple ,
treatment of Parallels , Ratio , and Limits . The changes are not sufficient to
prevent the simultaneous use of the old and new editions in the class ; still they
are ...
In this edition I have endeavored to present a more rigorous , but not less simple ,
treatment of Parallels , Ratio , and Limits . The changes are not sufficient to
prevent the simultaneous use of the old and new editions in the class ; still they
are ...
Σελίδα 86
... small except by comparison . This relative magnitude is called their Ratio , and
this ratio is always an abstract number . When two quantities of the same kind are
measured by the same unit , their ratio is the ratio of their numerical measures .
... small except by comparison . This relative magnitude is called their Ratio , and
this ratio is always an abstract number . When two quantities of the same kind are
measured by the same unit , their ratio is the ratio of their numerical measures .
Σελίδα 87
Hence , an incommensurable ratio is the limit toward which its successive
approximate values are constantly tending . ON THE THEORY OF LIMITS . 196 .
Def . When a quantity is regarded as having a fixed value , it is called a Constant ;
but ...
Hence , an incommensurable ratio is the limit toward which its successive
approximate values are constantly tending . ON THE THEORY OF LIMITS . 196 .
Def . When a quantity is regarded as having a fixed value , it is called a Constant ;
but ...
Σελίδα 89
If two variables be in a constant ratio , their limits are in the same ratio . For , let x
and y be two variables having the constant ratio r , then - = r , or , r = r y , therefore
lim . ( x ) – lim . ( x ) = lim . ( r y ) = r X lim . ( y ) , therefore = r . ore Tim .
If two variables be in a constant ratio , their limits are in the same ratio . For , let x
and y be two variables having the constant ratio r , then - = r , or , r = r y , therefore
lim . ( x ) – lim . ( x ) = lim . ( r y ) = r X lim . ( y ) , therefore = r . ore Tim .
Σελίδα 91
PROPOSITION XII . THEOREM . 200 . In the same circle , or equal circles , two
commensurable arcs have the same ratio as the angles which they subtend at
the centre . f B H . - - - - - - > 0 P In the circle APC let the two arcs be A B and AC ,
and ...
PROPOSITION XII . THEOREM . 200 . In the same circle , or equal circles , two
commensurable arcs have the same ratio as the angles which they subtend at
the centre . f B H . - - - - - - > 0 P In the circle APC let the two arcs be A B and AC ,
and ...
Τι λένε οι χρήστες - Σύνταξη κριτικής
Δεν εντοπίσαμε κριτικές στις συνήθεις τοποθεσίες.
Άλλες εκδόσεις - Προβολή όλων
Συχνά εμφανιζόμενοι όροι και φράσεις
acute adjacent altitude arc A B base bisect called centre chord circle circumference circumscribed coincide common Cons construct contained COROLLARY describe diagonals diameter difference direction divided Draw equal distances equal respectively equilateral equivalent erected extremities fall figure formed four given given line greater homologous sides hypotenuse included inscribed intersect isosceles joining less Let A B limit line A B lines drawn mean measured meet middle point multiplied one-half opposite sides parallelogram perimeter perpendicular plane position PROBLEM proportional prove Q. E. D. PROPOSITION quantities radii radius equal ratio rect rectangles regular polygon right angles segment shortest Show similar similar polygons square straight line Substitute subtend surface symmetrical tangent THEOREM triangle variable vertex vertices
Δημοφιλή αποσπάσματα
Σελίδα 30 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz.
Σελίδα 116 - To describe an isosceles triangle having each of the angles at the base double of the third angle.
Σελίδα 126 - The first of four magnitudes is said to have the same ratio to the second which the third has to the fourth, when...
Σελίδα 197 - Construct a rectangle having the difference of its base and altitude equal to a given line, and its area equivalent to the sum of a given triangle and a given pentagon.
Σελίδα 192 - In any proportion, the product of the means is equal to the product of the extremes.
Σελίδα 132 - If a line divides two sides of a triangle proportionally, it is parallel to the third side.
Σελίδα 165 - Any two rectangles are to each other as the products of their bases by their altitudes.
Σελίδα 62 - Every point in the bisector of an angle is equally distant from the sides of the angle ; and every point not in the bisector, but within the angle, is unequally distant from the sides of the angle.
Σελίδα 63 - A CIRCLE is a plane figure bounded by a curved line, all the points of which are equally distant from a point within called the centre; as the figure ADB E.
Σελίδα 136 - 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. A D A' Hyp. In triangles ABC and A'B'C', To prove AABC A A'B'C' A'B' x A'C ' Proof. Draw the altitudes BD and B'D'.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry |
| Συγγραφέας | George Albert Wentworth |
| Εκδότης | Ginn and Heath, 1881 |
| Πρωτότυπο από | Πανεπιστήμιο Χάρβαρντ |
| Ψηφιοποιήθηκε στις | 28 Φεβ. 2007 |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |