Elements of Geometry: With, Practical Applications |
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Αποτελέσματα 1 - 5 από τα 26.
Σελίδα 98
Any two rectangles are to each other as the product of their bases multiplied by
their altitudes . K D Let ABCD , AFGH be two rectangles , then will F B A G H
ABCD : AFGH :: ABX AD : AH X AF . Having placed the two rectangles so that the
...
Any two rectangles are to each other as the product of their bases multiplied by
their altitudes . K D Let ABCD , AFGH be two rectangles , then will F B A G H
ABCD : AFGH :: ABX AD : AH X AF . Having placed the two rectangles so that the
...
Σελίδα 100
... to denote the product of a number multiplied by itself . The squares of the
numbers 1 , 2 , 3 , & c . , are 1 , 4 , 9 , & c . From which we see that the square
formed on a line of double length is quadruple ; on a line of triple length it is nine
times as ...
... to denote the product of a number multiplied by itself . The squares of the
numbers 1 , 2 , 3 , & c . , are 1 , 4 , 9 , & c . From which we see that the square
formed on a line of double length is quadruple ; on a line of triple length it is nine
times as ...
Σελίδα 101
For , the triangle ABC is half the parallelogram ABCF , ( B. II , Prop . III . ) B D The
parallelogram is measured by the base BC multiplied into the altitude AD ;
therefore , the triangle is measured by the base BC into half the altitude AD . 1
Cor .
For , the triangle ABC is half the parallelogram ABCF , ( B. II , Prop . III . ) B D The
parallelogram is measured by the base BC multiplied into the altitude AD ;
therefore , the triangle is measured by the base BC into half the altitude AD . 1
Cor .
Σελίδα 217
... three dimensions of another parallelopipedon are valued according to the
same linear unit , and multiplied together in the same manner , the two products
will be to each other as the solids , and will serve to express their relative
magnitude .
... three dimensions of another parallelopipedon are valued according to the
same linear unit , and multiplied together in the same manner , the two products
will be to each other as the solids , and will serve to express their relative
magnitude .
Σελίδα 218
... in the first place , any parallelopipedon , ( B. VII , Prop . VII , ) is equal to a
rectangular parallelopipedon having the same altitude and an equal base . Now
the solidity of the latter is equal to its base multiplied 218 ELEMENTS OF
GEOMETRY .
... in the first place , any parallelopipedon , ( B. VII , Prop . VII , ) is equal to a
rectangular parallelopipedon having the same altitude and an equal base . Now
the solidity of the latter is equal to its base multiplied 218 ELEMENTS OF
GEOMETRY .
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle base bisect called centre chord circ circle circumference circumscribed coincide common cone consequently construction contained convex corresponding cylinder denote described diagonal diameter difference distance divided double draw equal equilateral equivalent exterior angle extremities figure follows formed four given gives greater hence included inscribed intersection join length less lines drawn magnitude manner mean measured measured by half meet multiplied opposite parallel parallel planes parallelogram parallelopipedon pass perimeter perpendicular plane plane MN polygon portion position prism PROBLEM produced Prop proportional PROPOSITION pyramid radii radius ratio rectangle remain respectively right-angles sector segment shown sides similar solid angle sphere spherical square straight line suppose surface taken tangent THEOREM third triangle ABC vertex VIII whole zone
Δημοφιλή αποσπάσματα
Σελίδα 231 - THE sphere is a solid terminated by a curve surface, all the points of which are equally distant from a point within, called the centre.
Σελίδα 147 - PROBLEM. To inscribe a circle in a given triangle. Let ABC be the given triangle : it is required to inscribe a circle in the triangle ABC.
Σελίδα 17 - A circle is a plane figure contained by one line, which is called the circumference, and is such, that all straight lines drawn from a certain point within the figure to the circumference are equal to one another.
Σελίδα 28 - If two sides and the included angle of the one are respectively equal to two sides and the included angle of the other...
Σελίδα 233 - The volume of a cylinder is equal to the product of its base by its altitude. Let the volume of the cylinder be denoted by V, its base by B, and its altitude by H.
Σελίδα 276 - THEOREM. Two triangles on the same sphere, or on equal spheres, are equal in all their parts, when they have each an equal angle included between equal sides. Suppose the side...
Σελίδα 120 - 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. D c A' D' Hyp. In triangles ABC and A'B'C', ZA = ZA'. To prove AABC = ABxAC. A A'B'C' A'B'xA'C' Proof. Draw the altitudes BD and B'D'.
Σελίδα 18 - If equals be added to unequals, the wholes are unequal. V. If equals be taken from unequals, the remainders are unequal. VI. Things which are double of the same, are equal to one another.
Σελίδα 232 - A spherical triangle is a portion of the surface of a sphere, bounded by three arcs of great circles.
Σελίδα 96 - Similar figures, are those that have all the angles of the one equal to all the angles of the other, each to each, and the sides about the equal angles proportional.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: With, Practical Applications |
| Συγγραφέας | George Roberts Perkins |
| Εκδότης | D. Appleton and Company, 1850 |
| Πρωτότυπο από | Πανεπιστήμιο Χάρβαρντ |
| Ψηφιοποιήθηκε στις | 1 Μαρ. 2007 |
| Μέγεθος | 320 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |