Elements of Geometry: With, Practical Applications |
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Σελίδα 17
The line passing through the centre , and terminating each way in the
circumference , is called a diameter . ( 25. ) A circle might be defined as a plane
figure bounded by a line , all the parts of which have the same degree of flexure .
The line passing through the centre , and terminating each way in the
circumference , is called a diameter . ( 25. ) A circle might be defined as a plane
figure bounded by a line , all the parts of which have the same degree of flexure .
Σελίδα 71
If two concentric circles be described , then , from whatever point in the
circumference of the one , lines be drawn to the extremity of any diameter of the
other , the sum of their squares will always be the same . Let D be the common
centre of ...
If two concentric circles be described , then , from whatever point in the
circumference of the one , lines be drawn to the extremity of any diameter of the
other , the sum of their squares will always be the same . Let D be the common
centre of ...
Σελίδα 85
... are respectively measured by the arcs CG , CL , which make half the
circumference , LG being a diameter . Cor . 2. Hence , also , one right - angle
must have for its measure a quarter of the circumference . PROPOSITION VII .
THEOREM .
... are respectively measured by the arcs CG , CL , which make half the
circumference , LG being a diameter . Cor . 2. Hence , also , one right - angle
must have for its measure a quarter of the circumference . PROPOSITION VII .
THEOREM .
Σελίδα 92
Hence , when the given angle K is a right - angle , the line AB will be a diameter ;
and when the angle K is acute , then will the angle ALB be obtuse . When the
given angle K is obtuse , if we find a segment capable of containing the angle ...
Hence , when the given angle K is a right - angle , the line AB will be a diameter ;
and when the angle K is acute , then will the angle ALB be obtuse . When the
given angle K is obtuse , if we find a segment capable of containing the angle ...
Σελίδα 94
Such is the ratio of the circumference of a circle to its diameter , the diagonal of a
square to its side , etc. Hence many have deemed the arithmetical method not
sufficiently general to apply to geometry . This would be a safe inference , were it
...
Such is the ratio of the circumference of a circle to its diameter , the diagonal of a
square to its side , etc. Hence many have deemed the arithmetical method not
sufficiently general to apply to geometry . This would be a safe inference , were it
...
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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 |