Elements of Geometry: With, Practical Applications |
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Σελίδα 13
Two straight lines are said to be parallel , when , being situated in the same
plane , they cannot meet , how far soever , either way , both of them be produced
. They are obviously everywhere equally distant . ( 21. ) Another definition of
parallel ...
Two straight lines are said to be parallel , when , being situated in the same
plane , they cannot meet , how far soever , either way , both of them be produced
. They are obviously everywhere equally distant . ( 21. ) Another definition of
parallel ...
Σελίδα 14
All fabrics produced in the loom consist of two systems of parallel threads ,
crossing each other at rightangles , so interlaced as to give strength and firmness
to the cloth . The railway consists of two or more parallel lines of iron bars , called
rails ...
All fabrics produced in the loom consist of two systems of parallel threads ,
crossing each other at rightangles , so interlaced as to give strength and firmness
to the cloth . The railway consists of two or more parallel lines of iron bars , called
rails ...
Σελίδα 27
It also appears that every equilateral triangle is equiangular , or has all its angles
equal . PROPOSITION VI . THEOREM . When one side of a triangle is produced ,
the exterior angle is greater than either of the two interior and opposite angles .
It also appears that every equilateral triangle is equiangular , or has all its angles
equal . PROPOSITION VI . THEOREM . When one side of a triangle is produced ,
the exterior angle is greater than either of the two interior and opposite angles .
Σελίδα 41
Cor . 2. If a line , cutting two other lines , make the sum of the two interior angles ,
on the same side , less than two right - angles , those two lines will not be parallel
, and consequently will ineet each other when produced . PROPOSITION XXI .
Cor . 2. If a line , cutting two other lines , make the sum of the two interior angles ,
on the same side , less than two right - angles , those two lines will not be parallel
, and consequently will ineet each other when produced . PROPOSITION XXI .
Σελίδα 42
When each side of a polygonal figure is produced , in the same direction , the
sum of all the exterior angles will be equal to four right - angles . For , if from any
point in the same plane , straight lines be drawn parallel to the sides of the figure
...
When each side of a polygonal figure is produced , in the same direction , the
sum of all the exterior angles will be equal to four right - angles . For , if from any
point in the same plane , straight lines be drawn parallel to the sides of the figure
...
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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 |