Elements of Geometry |
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Σελίδα
Thus a rectangle with a constant base b , and a variable altitude X , will afford an
obvious illustration of the axiomatic truth contained in [ 4 ] , page 88 . If x increase
and approach the altitude a as a limit , the area of the rectangle increases and ...
Thus a rectangle with a constant base b , and a variable altitude X , will afford an
obvious illustration of the axiomatic truth contained in [ 4 ] , page 88 . If x increase
and approach the altitude a as a limit , the area of the rectangle increases and ...
Σελίδα 86
Two quantities are commensurable if there be some third quantity of the same
kind which is contained an exact number of times in each . This third quantity is
called the common measure of these quantities , and each of the given quantities
is ...
Two quantities are commensurable if there be some third quantity of the same
kind which is contained an exact number of times in each . This third quantity is
called the common measure of these quantities , and each of the given quantities
is ...
Σελίδα 87
Again , if each of these equal parts of b be divided into n equal parts ; that is , if b
be divided into na equal parts , and if one of these parts be contained m ' times in
a with a remainder less than part of b , then is a nearer approximate value of the ...
Again , if each of these equal parts of b be divided into n equal parts ; that is , if b
be divided into na equal parts , and if one of these parts be contained m ' times in
a with a remainder less than part of b , then is a nearer approximate value of the ...
Σελίδα 90
In the application of the principles of limits , reference to this section ( § 199 ) will
always include the fundamental truth of limits contained in Proposition I . ; and it
will be left as an exercise for the student to determine in each case what other ...
In the application of the principles of limits , reference to this section ( § 199 ) will
always include the fundamental truth of limits contained in Proposition I . ; and it
will be left as an exercise for the student to determine in each case what other ...
Σελίδα 91
Suppose H K to be contained in A B three times , and in A C five times . arc A B 3
Then arc A C5 At the several points of division on A B and A C draw radii . These
radii will divide Z AOC into five equal parts , of which Z AO B will contain three ...
Suppose H K to be contained in A B three times , and in A C five times . arc A B 3
Then arc A C5 At the several points of division on A B and A C draw radii . These
radii will divide Z AOC into five equal parts , of which Z AO B will contain three ...
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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 |