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 88
165 ) , the circumferences of the circles whose radii are CA and OB , we say that
circ . CA : circ . OB :: CA : OB . For , if this proportion be not true , CA will be to OB
as circ . CA is to a fourth term either greater or less than circ . OB .
165 ) , the circumferences of the circles whose radii are CA and OB , we say that
circ . CA : circ . OB :: CA : OB . For , if this proportion be not true , CA will be to OB
as circ . CA is to a fourth term either greater or less than circ . OB .
Σελίδα 89
It follows , moreover , from what has been said , that CA cannot be to OB as circ .
CA is to a circumference greater than circ . OB ; for , if this were the case , we
should have hy inversion , OB : CA :: a circumference greater than circ . OB : circ .
It follows , moreover , from what has been said , that CA cannot be to OB as circ .
CA is to a circumference greater than circ . OB ; for , if this were the case , we
should have hy inversion , OB : CA :: a circumference greater than circ . OB : circ .
Σελίδα 90
The area of a circle is equal to the product of its circumference by half of the
radius . Demonstration . Denoting by surf . CA the surface or area of a circle
whose radius is CA , we say that surf . CA = CA x circ . CA. Fig . 167. If į CA x circ .
CA ( fig .
The area of a circle is equal to the product of its circumference by half of the
radius . Demonstration . Denoting by surf . CA the surface or area of a circle
whose radius is CA , we say that surf . CA = CA x circ . CA. Fig . 167. If į CA x circ .
CA ( fig .
Σελίδα 91
than { CB x circ . CB . This last quantity is , by hypothesis , the measure of the
circle of which CA is the radius ; consequently the polygon would be less than the
inscribed circle , which is absurd ; it is impossible then that the circumference of a
...
than { CB x circ . CB . This last quantity is , by hypothesis , the measure of the
circle of which CA is the radius ; consequently the polygon would be less than the
inscribed circle , which is absurd ; it is impossible then that the circumference of a
...
Σελίδα 165
But EH + GF is the same as EF + GH ; therefore the arc GH , which measures the
angle A , is equal to a semicircumference minus the side EF ; likewise the angle
B has for its measure circ . — DF , and the angle C , 1 circ . — DE . This property ...
But EH + GF is the same as EF + GH ; therefore the arc GH , which measures the
angle A , is equal to a semicircumference minus the side EF ; likewise the angle
B has for its measure circ . — DF , and the angle C , 1 circ . — DE . This property ...
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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 |