Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New England |
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Σελίδα 3
A diagonal is a line which joins the vertices of two angles not adjacent , as AC (
fig . 42 ) . 19. An equilateral polygon is one which has all its sides equal ; an
equiangular polygon is one which has all its angles equal . 20. Two polygons are
...
A diagonal is a line which joins the vertices of two angles not adjacent , as AC (
fig . 42 ) . 19. An equilateral polygon is one which has all its sides equal ; an
equiangular polygon is one which has all its angles equal . 20. Two polygons are
...
Σελίδα 19
42 . polygon ; if from the vertex of the angle A we draw to the vertices of the
opposite angles the diagonals AC , AD , AE , & c . , it is evident , that the polygon
will be divided into five triangles , if it have seven sides , and into six , if it have
eight ...
42 . polygon ; if from the vertex of the angle A we draw to the vertices of the
opposite angles the diagonals AC , AD , AE , & c . , it is evident , that the polygon
will be divided into five triangles , if it have seven sides , and into six , if it have
eight ...
Σελίδα 22
An inscribed triangle is a triangle whose three angles have their vertices in the
circumference of the circle , as BAC . * In common discourse the circle is
sometimes confounded with its circumference ; but it will always be easy to
preserve the ...
An inscribed triangle is a triangle whose three angles have their vertices in the
circumference of the circle , as BAC . * In common discourse the circle is
sometimes confounded with its circumference ; but it will always be easy to
preserve the ...
Σελίδα 23
And in general an inscribed figure is one , all whose angles have their vertices in
the circumference of the circle . In this case , the circle is said to be circumscribed
about the figure . 96. A secant is a line , which meets the circumference in two ...
And in general an inscribed figure is one , all whose angles have their vertices in
the circumference of the circle . In this case , the circle is said to be circumscribed
about the figure . 96. A secant is a line , which meets the circumference in two ...
Σελίδα 30
61 ) , the vertices of which are at the centre , intercept upon the circumference
equal arcs AB , DE . Reciprocally , if the arcs AB , DE , are equal , the angles ACB
, DCE , also will be equal . Demonstration . i . If the angle ACB is equal to the ...
61 ) , the vertices of which are at the centre , intercept upon the circumference
equal arcs AB , DE . Reciprocally , if the arcs AB , DE , are equal , the angles ACB
, DCE , also will be equal . Demonstration . i . If the angle ACB is equal to the ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABC fig ABCD adjacent altitude angle ACB applied base called centre chord circ circle circumference circumscribed common cone consequently considered construction contained Corollary cylinder Demonstration described diameter difference distance divided draw drawn entire equal equivalent example extremities faces figure follows formed four given greater half hence homologous sides inclination inscribed join less let fall manner mean measure meet moreover multiplied namely opposite parallel parallelogram parallelopiped pass perimeter perpendicular plane plane angles polyedron polygon prism PROBLEM proportional proposition pyramid radii radius ratio reason rectangle regular polygon remain respect right angles Scholium sector segment side BC sides similar solid angle Solution sphere spherical triangle square straight line suppose surface taken THEOREM third triangle ABC vertex vertices whence
Δημοφιλή αποσπάσματα
Σελίδα ii - Co. of the said district, have deposited in this office the title of a book, the right whereof they claim as proprietors, in the words following, to wit : " Tadeuskund, the Last King of the Lenape. An Historical Tale." In conformity to the Act of the Congress of the United States...
Σελίδα 9 - If two triangles have the three sides of the one equal to the three sides of the other, each to each, the triangles are congruent.
Σελίδα 63 - The square of the hypothenuse is equal to the sum of the squares of the other two sides ; as, 5033 402+302.
Σελίδα 9 - Hence a straight line drawn from the vertex of an isosceles triangle, to the middle of the base, is perpendicular to that base, and divides the vertical angle into two equal parts.
Σελίδα ii - States entitled an act for the encouragement of learning hy securing the copies of maps, charts and books to the author., and proprietors of such copies during the times therein mentioned, and also to an act entitled an act supplementary to an act, entitled an act for the encouragement of learning by securing the copies of maps, charts and books to the authors and proprietors of such copies during the times therein mentioned and extending the benefits thereof to the arts of designing, engraving and...
Σελίδα 61 - 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'.
Σελίδα 166 - In any spherical triangle, the greater side is opposite the greater angle ; and conversely, the greater angle is opposite the greater side.
Σελίδα 153 - 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 25 - Two equal chords are equally distant from the centre ; and of two unequal chords, the less is at the greater distance from the centre.
Σελίδα 164 - If two triangles have two sides and the inchtded angle of the one respectively equal to two sides and the included angle of the other, the two triangles are equal in all respects.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry...: Translated from the French for the Use of the Students of the University at Cambridge, New England |
| Συγγραφείς | Adrien Marie Legendre, John Farrar |
| Έκδοση | 2 |
| Εκδότης | Hilliard and Metcalf, 1825 |
| Πρωτότυπο από | η Δημόσια Βιβλιοθήκη της Νέας Υόρκης |
| Ψηφιοποιήθηκε στις | 21 Ιουν. 2006 |
| Μέγεθος | 224 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |