Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |
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Σελίδα 68
to the less , which is impossible : Therefore G is not the centre of the circle ABC :
In the same manner , it can be shown , that no other point but F is the centre : that
is , F is the centre of the circle ABC : Which was to be found . Cor . From this it is ...
to the less , which is impossible : Therefore G is not the centre of the circle ABC :
In the same manner , it can be shown , that no other point but F is the centre : that
is , F is the centre of the circle ABC : Which was to be found . Cor . From this it is ...
Σελίδα 69
angle : Therefore each of the angles AFE , BFE is a right angle ; wherefore the
straight line CD , A B drawn through the centre bisecting AB , which does not
pass through the centre , cuts AB at right angles . Again , let CD cut AB at right
angles ...
angle : Therefore each of the angles AFE , BFE is a right angle ; wherefore the
straight line CD , A B drawn through the centre bisecting AB , which does not
pass through the centre , cuts AB at right angles . Again , let CD cut AB at right
angles ...
Σελίδα 70
Let the two circles ABC , CDG cut one another in the points B , C ; they have not
the same centre . For , if it be possible , let E be their centre : join EC , and draw
any straight line EFG meeting the circles in F and G : and because E is the centre
...
Let the two circles ABC , CDG cut one another in the points B , C ; they have not
the same centre . For , if it be possible , let E be their centre : join EC , and draw
any straight line EFG meeting the circles in F and G : and because E is the centre
...
Σελίδα 73
If a point be taken within a circle , from which there fall more than two equal
straight lines upon the circumference , that point is the centre of the circle . Let the
point D be taken within the circle ABC , from which there fall on the circumference
...
If a point be taken within a circle , from which there fall more than two equal
straight lines upon the circumference , that point is the centre of the circle . Let the
point D be taken within the circle ABC , from which there fall on the circumference
...
Σελίδα 76
G Take E the centre of the circle ABDC , and from it draw EF , EG , perpendiculars
to AB , CD ; join AE and EC . Then , because the straight line EF passing through
the centre , cuts the straight line AB , which does not pass through the centre at ...
G Take E the centre of the circle ABDC , and from it draw EF , EG , perpendiculars
to AB , CD ; join AE and EC . Then , because the straight line EF passing through
the centre , cuts the straight line AB , which does not pass through the centre at ...
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Συχνά εμφανιζόμενοι όροι και φράσεις
ABCD altitude angle ABC angle BAC arch base bisected Book called centre circle circle ABC circumference coincide common contained cosine cylinder definition demonstrated described diameter difference divided double draw drawn equal equal angles equiangular Euclid exterior extremity fall fore four fourth given given straight line greater half inscribed interior join less Let ABC magnitudes manner meet multiple opposite parallel parallelogram pass perpendicular plane polygon prism produced proportionals proposition proved Q. E. D. PROP radius ratio reason rectangle contained rectilineal figure right angles segment shewn sides similar sine solid square straight line taken tangent THEOR thing third touches triangle ABC wherefore whole
Δημοφιλή αποσπάσματα
Σελίδα 56 - If a straight line be divided into two equal parts, and also into two unequal parts; the rectangle contained by the unequal parts, together with the square of the line between the points of section, is equal to the square of half the line.
Σελίδα 19 - 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 33 - THE greater angle of every triangle is subtended by the greater side, or has the greater side opposite to it.
Σελίδα 62 - In every triangle, the square on the side subtending either of the acute angles, is less than the squares on the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the...
Σελίδα 62 - In obtuse-angled triangles, if a perpendicular be drawn from either of the acute angles to the opposite side produced, the square of the side subtending the obtuse angle, is greater than the squares of the sides containing the obtuse angle, by twice the rectangle contained by the side upon which, when produced, the perpendicular falls, and the straight line intercepted without the triangle, between the perpendicular and the obtuse angle. Let ABC be an obtuse-angled triangle, having the obtuse angle...
Σελίδα 130 - If two triangles have one angle of the one equal to one angle of the other and the sides about these equal angles proportional, the triangles are similar.
Σελίδα 76 - THE diameter is the greatest straight line in a circle; and, of all others, that which is nearer to the centre is always greater than one more remote ; and the greater is nearer to the centre than the less.* Let ABCD be a circle, of which...
Σελίδα 36 - IF two triangles have two sides of the one equal to two sides of the other, each to each, but the angle contained by the two sides of one of them greater than the angle contained by the two sides equal to them, of the other ; the base of that which has the greater angle shall be greater than the base of the other.
Σελίδα 18 - When a straight line standing on another straight line makes the adjacent angles equal to one another, each of the angles is called a right angle ; and the straight line which stands on the other is called a perpendicular to it.
Σελίδα 55 - If a straight line be divided into any two parts, the rectangle contained by the whole and one of the parts, is equal to the rectangle contained by the two parts, together with the square of the aforesaid part.
Πληροφορίες βιβλιογραφίας
| Τίτλος | Elements of Geometry: Containing the First Six Books of Euclid, with a Supplement on the Quadrature of the Circle, and the Geometry of Solids; to which are Added Elements of Plane and Spherical Trigonometry |
| Συγγραφέας | John Playfair |
| Επιμελητής | John Playfair |
| Μεταφράστηκε από | John Playfair |
| Έκδοση | 5 |
| Εκδότης | G. Long, 1819 |
| Πρωτότυπο από | το Πανεπιστήμιο του Μίτσιγκαν |
| Ψηφιοποιήθηκε στις | 11 Ιουν. 2007 |
| Μέγεθος | 333 σελίδες |
| Εξαγωγή αναφοράς | BiBTeX EndNote RefMan |