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 vii
The fourth section of the second part treats of the three round bodies , which are
the sphere , the cone , and the cylinder . The measure of the surfaces and
solidities of these bodies is determined by a method analogous to that of
Archimedes ...
The fourth section of the second part treats of the three round bodies , which are
the sphere , the cone , and the cylinder . The measure of the surfaces and
solidities of these bodies is determined by a method analogous to that of
Archimedes ...
Σελίδα 175
We call a cone the solid generated by the revolution of a right - angled ... side
S.A. In this revolution the side AB describes a circular plane BDCE called the
base of the cone , and the hypothenuse SB describes the convex surface of the
cone .
We call a cone the solid generated by the revolution of a right - angled ... side
S.A. In this revolution the side AB describes a circular plane BDCE called the
base of the cone , and the hypothenuse SB describes the convex surface of the
cone .
Σελίδα 176
Two cylinders or two cones are similar , when their axes are to each other as the
diameters of their bases . Fig . 252 . 511. If , in the circle ACD ( fig . 252 ) ,
considered as the base of a cylinder , a polygon ABCDE be inscribed , and upon
the ...
Two cylinders or two cones are similar , when their axes are to each other as the
diameters of their bases . Fig . 252 . 511. If , in the circle ACD ( fig . 252 ) ,
considered as the base of a cylinder , a polygon ABCDE be inscribed , and upon
the ...
Σελίδα 177
... a surface that cannot be met by a straight line in more than two points ; still it is
possible that a straight line may apply itself exactly to a convex surface in a
certain direction ; we have examples of this in the surfaces of the cone and
cylinder .
... a surface that cannot be met by a straight line in more than two points ; still it is
possible that a straight line may apply itself exactly to a convex surface in a
certain direction ; we have examples of this in the surfaces of the cone and
cylinder .
Σελίδα 181
... of the surface of a greater cylinder . We conclude then that the convex surface
of a cylinder is equal to the circumference of the base multiplied by its altitude .
THEOREM . 524. The solidity of a cone is equal Of the Three Round Bodies . 181
.
... of the surface of a greater cylinder . We conclude then that the convex surface
of a cylinder is equal to the circumference of the base multiplied by its altitude .
THEOREM . 524. The solidity of a cone is equal Of the Three Round Bodies . 181
.
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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 |