Elements of Geometry: With, Practical Applications |
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Σελίδα 63
When they wished to ascertain whether the angle formed by the meeting of two
sticks of timber was a right - angle , they measured frorn the angular point on the
one stick 6 feet , and on the other 8 feet ; then if the ten - foot pole would reach ...
When they wished to ascertain whether the angle formed by the meeting of two
sticks of timber was a right - angle , they measured frorn the angular point on the
one stick 6 feet , and on the other 8 feet ; then if the ten - foot pole would reach ...
Σελίδα 78
Hence the angles at the centre are measured by the arcs included between their
sides . 14. Similar arcs , similar sectors , and similar segments are such as
correspond with equal angles at the centres of their respective circles .
PROPOSITION ...
Hence the angles at the centre are measured by the arcs included between their
sides . 14. Similar arcs , similar sectors , and similar segments are such as
correspond with equal angles at the centres of their respective circles .
PROPOSITION ...
Σελίδα 84
The angle formed by a tangent and chord is measured by half the urc of that
chord . A В. G K D Let AB be a tangent , and CD a chord drawn from the point of
contact C ; then the angle BCD will be measured by half the arc CGD , and the
angle ...
The angle formed by a tangent and chord is measured by half the urc of that
chord . A В. G K D Let AB be a tangent , and CD a chord drawn from the point of
contact C ; then the angle BCD will be measured by half the arc CGD , and the
angle ...
Σελίδα 85
Now , the former of these , CFL , being an angle at the centre , is measured by the
arc CL , which is half the arc CLD ; therefore , the angle DCA is also measured by
half the arc CLD . Cor . 1. The sum of two right - angles is measured by half ...
Now , the former of these , CFL , being an angle at the centre , is measured by the
arc CL , which is half the arc CLD ; therefore , the angle DCA is also measured by
half the arc CLD . Cor . 1. The sum of two right - angles is measured by half ...
Σελίδα 86
difference of those angles is measured by half the difference of the said arcs ; that
is , the angle BAC is meas' ured by half the arc BC upon which it stands . Cor . 1.
All angles in the same segment of a circle , or subtended by the same arc , are ...
difference of those angles is measured by half the difference of the said arcs ; that
is , the angle BAC is meas' ured by half the arc BC upon which it stands . Cor . 1.
All angles in the same segment of a circle , or subtended by the same arc , are ...
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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 |