Elements of Geometry: With, Practical Applications |
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Αποτελέσματα 1 - 5 από τα 33.
Σελίδα 23
Join CD , and bisect it by the perpendicular FG ; then will the point G be the point
sought . For , if we join GC , GD , we shall have the triangle GFC equal to GFD ,
since the side FC is equal to FD , the side FG common , and the angle CFG equal
...
Join CD , and bisect it by the perpendicular FG ; then will the point G be the point
sought . For , if we join GC , GD , we shall have the triangle GFC equal to GFD ,
since the side FC is equal to FD , the side FG common , and the angle CFG equal
...
Σελίδα 24
Join CB , and bisect it by the perpendicular DF ; then will F be the point at which
the tree must break . For , joining BF , and comparing the triangle FBD with the
triangle FCD , we see that the side DB is equal to DC , the side FD common , and
...
Join CB , and bisect it by the perpendicular DF ; then will F be the point at which
the tree must break . For , joining BF , and comparing the triangle FBD with the
triangle FCD , we see that the side DB is equal to DC , the side FD common , and
...
Σελίδα 25
F Construction . Make AB equal to the given base ; draw AC , making the angle
BAC equal to the given angle , and AC equal to the sum of the other two sides ;
join BC , and bisect it by the perpendicular DF ; finally , join BF , and ABF will be
the ...
F Construction . Make AB equal to the given base ; draw AC , making the angle
BAC equal to the given angle , and AC equal to the sum of the other two sides ;
join BC , and bisect it by the perpendicular DF ; finally , join BF , and ABF will be
the ...
Σελίδα 26
... the angle 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 angle 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 ...
Σελίδα 32
To bisect a given angle ABC . Take any equal distances , BA , BC , B on the ...
any equal radii , describe arcs intersecting each Α . other at D ; then , BD being
drawn , it will bisect the angle ABC . For , drawing AD , CD , the three sides of the
...
To bisect a given angle ABC . Take any equal distances , BA , BC , B on the ...
any equal radii , describe arcs intersecting each Α . other at D ; then , BD being
drawn , it will bisect the angle ABC . For , drawing AD , CD , the three sides of the
...
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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 |