Elements of Geometry: With, Practical Applications |
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Σελίδα 42
A convex polygon may be defined to be one such that no side , by being
produced in either direction , can divide the polygon . The polygon ABCDFG is
not convex , since it may be divided by producing either of the sides CD or FD .
A convex polygon may be defined to be one such that no side , by being
produced in either direction , can divide the polygon . The polygon ABCDFG is
not convex , since it may be divided by producing either of the sides CD or FD .
Σελίδα 43
PROPOSITION XXIV . convex F / F a 7 THEOREM . In any convex polygon , the
sum of all the interior angles , taken together , is equal to twice as many right -
angles as the polygon has sides , wanting four right - angles . Let ABCDFG be a ...
PROPOSITION XXIV . convex F / F a 7 THEOREM . In any convex polygon , the
sum of all the interior angles , taken together , is equal to twice as many right -
angles as the polygon has sides , wanting four right - angles . Let ABCDFG be a ...
Σελίδα 44
For , drawing CD ' and FD ' respecD ' tively parallel to DF and DC , we shall form
a parallelogram CDFD ' ; and the figure ABCD'FG will be a convex polygon ,
having the same number of sides as the original polygon . And it is moreover ...
For , drawing CD ' and FD ' respecD ' tively parallel to DF and DC , we shall form
a parallelogram CDFD ' ; and the figure ABCD'FG will be a convex polygon ,
having the same number of sides as the original polygon . And it is moreover ...
Σελίδα 199
This demonstration is founded on the supposition that the solid angle is convex ,
or that the plane of no one surface produced can ever meet the solid angle . If it
were otherwise , the sum of the plane angles would no longer be limited , and ...
This demonstration is founded on the supposition that the solid angle is convex ,
or that the plane of no one surface produced can ever meet the solid angle . If it
were otherwise , the sum of the plane angles would no longer be limited , and ...
Σελίδα 202
The other planes or parallelograms , taken together , constitute the lateral or
convex surface of the prism . 3. The altitude of a prism is the perpendicular
distance between its bases ; and its length is a line equal to any one of its lateral
edges ...
The other planes or parallelograms , taken together , constitute the lateral or
convex surface of the prism . 3. The altitude of a prism is the perpendicular
distance between its bases ; and its length is a line equal to any one of its lateral
edges ...
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Elements of Geometry with Practical Applications George R. Perkins Δεν υπάρχει διαθέσιμη προεπισκόπηση - 2019 |
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 |