Elements of Geometry: With, Practical Applications |
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Σελίδα 181
A line is parallel to a plane , when , if both are produced to any distance , they do
not meet ; and , conversely , the plane is then also parallel to the line . 6. Two
planes are parallel to each other , when , both being produced to any distance ...
A line is parallel to a plane , when , if both are produced to any distance , they do
not meet ; and , conversely , the plane is then also parallel to the line . 6. Two
planes are parallel to each other , when , both being produced to any distance ...
Σελίδα 189
are parallel to each other . For , conceive a plane perpendicular to the line C : the
lines A and B , being parallel to C , will be perpendicular to the same plane ;
therefore , by the preceding corollary , they will be parallel to each other . When
the ...
are parallel to each other . For , conceive a plane perpendicular to the line C : the
lines A and B , being parallel to C , will be perpendicular to the same plane ;
therefore , by the preceding corollary , they will be parallel to each other . When
the ...
Σελίδα 190
A N P B Let the planes M. MN and PQ be each perpendicular to AB ; then will
they be parallel . For , if they can meet anywhere , let Q o be one of their common
points , and join OA , OB . The line AB , which is perpendicular to the plane MN ,
is ...
A N P B Let the planes M. MN and PQ be each perpendicular to AB ; then will
they be parallel . For , if they can meet anywhere , let Q o be one of their common
points , and join OA , OB . The line AB , which is perpendicular to the plane MN ,
is ...
Σελίδα 191
PQ , in which those lines are situated , would also meet therefore the planes
would not be parallel . PROPOSITION XI , THEOREM . A line which is
perpendicular to one of two parallel planes , is perpendicular to the other also . M
-D N B Let the ...
PQ , in which those lines are situated , would also meet therefore the planes
would not be parallel . PROPOSITION XI , THEOREM . A line which is
perpendicular to one of two parallel planes , is perpendicular to the other also . M
-D N B Let the ...
Σελίδα 192
With, Practical Applications George Roberts Perkins. E M N G P Q H Let EG , FH
be two parallel lines included between the two parallel planes MN , PQ ; then will
these lines be equal . Through the parallels EG , FH , draw the plane EGHF to ...
With, Practical Applications George Roberts Perkins. E M N G P Q H Let EG , FH
be two parallel lines included between the two parallel planes MN , PQ ; then will
these lines be equal . Through the parallels EG , FH , draw the plane EGHF to ...
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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 |