Elements of Geometry: With, Practical Applications |
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Σελίδα 8
With, Practical Applications George Roberts Perkins. IV . A point is not a
magnitude . It has no dimension in any direction , but simply position . Hence , the
extremities of lines are points . Also , the place of intersection of two lines is a
point . ( 2. ) ...
With, Practical Applications George Roberts Perkins. IV . A point is not a
magnitude . It has no dimension in any direction , but simply position . Hence , the
extremities of lines are points . Also , the place of intersection of two lines is a
point . ( 2. ) ...
Σελίδα 20
Hence , also , conversely , if the two angles ADC , BDC , on the same side of the
line AB , make up together two right - angles , then AD and DB will form a
continued straight line AB . Cor . 2. Hence , all the angles which can be made at
any ...
Hence , also , conversely , if the two angles ADC , BDC , on the same side of the
line AB , make up together two right - angles , then AD and DB will form a
continued straight line AB . Cor . 2. Hence , all the angles which can be made at
any ...
Σελίδα 23
11 :) hence the angle BGD is equal to AGC . Which is necessary , that the angle
of incidence and the angle of reflection of the light may be equal . ( 30. ) Suppose
AC and BD to represent two trees standing on the horizontal plane AB , it is ...
11 :) hence the angle BGD is equal to AGC . Which is necessary , that the angle
of incidence and the angle of reflection of the light may be equal . ( 30. ) Suppose
AC and BD to represent two trees standing on the horizontal plane AB , it is ...
Σελίδα 26
... ACD equal to the angle BCD ; and the side CD common ; therefore the two
triangles are identical , or equal in all respects , ( Prop . 111 , ) and consequently
the angle B is equal to the angle A. Cor . 1. Hence the line which bisects the
vertical ...
... ACD equal to the angle BCD ; and the side CD common ; therefore the two
triangles are identical , or equal in all respects , ( Prop . 111 , ) and consequently
the angle B is equal to the angle A. Cor . 1. Hence the line which bisects the
vertical ...
Σελίδα 28
But a part cannot be equal to the whole ; ( Ax . VIII ; ) hence there can be no
inequality between the sides CB and CA , and therefore the triangle is isosceles .
PROPOSITION VIII . THEOREM . When two triangles have the 28 ELEMENTS OF
...
But a part cannot be equal to the whole ; ( Ax . VIII ; ) hence there can be no
inequality between the sides CB and CA , and therefore the triangle is isosceles .
PROPOSITION VIII . THEOREM . When two triangles have the 28 ELEMENTS OF
...
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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 |