Elements of Geometry |
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Αποτελέσματα 1 - 5 από τα 17.
Σελίδα 73
Every chord subtends two arcs whose sum is the circumference . Thus the chord
A B , ( Fig . 3 ) , subtends the arc A M B and the arc A D B . Whenever a chord and
its arc are spoken of , the less arc is meant unless it be otherwise stated . 167 .
Every chord subtends two arcs whose sum is the circumference . Thus the chord
A B , ( Fig . 3 ) , subtends the arc A M B and the arc A D B . Whenever a chord and
its arc are spoken of , the less arc is meant unless it be otherwise stated . 167 .
Σελίδα 78
CONVERSELY : In the same circle , or equal circles , equal arcs subtend equal
angles at the centre . In the equal circles ABP and A ' B ' P ' let arc RS = arc R ' S '
. We are to prove ZROS = R ' O ' S ' . Apply O A B P to O A ' B ' P ' , so that the ...
CONVERSELY : In the same circle , or equal circles , equal arcs subtend equal
angles at the centre . In the equal circles ABP and A ' B ' P ' let arc RS = arc R ' S '
. We are to prove ZROS = R ' O ' S ' . Apply O A B P to O A ' B ' P ' , so that the ...
Σελίδα 79
PROPOSITION V . THEOREM . 181 . In the same circle , or equal circles , equal
arcs are subtended by equal chords . S PY In the equal circles A B P and A ' B ' P
' let arc RS = arc R ' S . We are to prove chord RS = chord R ' S ' . Draw the radii ...
PROPOSITION V . THEOREM . 181 . In the same circle , or equal circles , equal
arcs are subtended by equal chords . S PY In the equal circles A B P and A ' B ' P
' let arc RS = arc R ' S . We are to prove chord RS = chord R ' S ' . Draw the radii ...
Σελίδα 80
George Albert Wentworth. PROPOSITION VI . THEOREM . 182 . CONVERSELY :
In the same circle , or equal circles , equal chords subtend equal arcs . PI In the
equal circles ABP and A ' B ' P ' , let chord RS = chord RS . We are to prove arc ...
George Albert Wentworth. PROPOSITION VI . THEOREM . 182 . CONVERSELY :
In the same circle , or equal circles , equal chords subtend equal arcs . PI In the
equal circles ABP and A ' B ' P ' , let chord RS = chord RS . We are to prove arc ...
Σελίδα 81
The radius perpendicular to a chord bisects the chord and the arc subtended by it
. Let A B be the chord , and let the radius C S be perpendicular to A B at the point
M . We are to prove AM = BM , and arc A S = arc B S . Draw C A and C B .
The radius perpendicular to a chord bisects the chord and the arc subtended by it
. Let A B be the chord , and let the radius C S be perpendicular to A B at the point
M . We are to prove AM = BM , and arc A S = arc B S . Draw C A and C B .
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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 |